In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
The N-periodic wave solvability problem for the N=1 supersymmetric Sawada–Kotera–Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function. The constraint equat...The N-periodic wave solvability problem for the N=1 supersymmetric Sawada–Kotera–Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function. The constraint equations and unknown parameters are redefined, and the numerical calculation process of the N-periodic wave solutions is derived. It has been verified that under certain conditions, the asymptotic relations between N-periodic wave solutions and N-soliton solutions can be established. Some numerical solutions of three-periodic wave are presented. Under the influence of the Grassmann variable, the three-periodic wave solutions will generate an influence band in the middle region, and the amplitude becomes bigger as the distance from the influence band increases.展开更多
We are concerned with a nonlinear elliptic equation,involving a Kirchhoff type nonlocal term and a potential V(x),onℝ3.As is well known that,even in,H_(r)^(1)(R^(3)),the nonlinear term is a pure power form of∣u∣^(p−...We are concerned with a nonlinear elliptic equation,involving a Kirchhoff type nonlocal term and a potential V(x),onℝ3.As is well known that,even in,H_(r)^(1)(R^(3)),the nonlinear term is a pure power form of∣u∣^(p−1)u and V(x)≡1,it seems very difficult to apply the mountain-pass theorem to get a solution(i.e.,mountain-pass solution)to this kind of equation for all p∈(1,5),due to the difficulty of verifying the boundedness of the PalaisSmale sequence obtained by the mountain-pass theorem when p∈(1,3).In this paper,we find a new strategy to overcome this difficulty,and then get a mountain-pass solution to the equation for all p∈(1,5)and for both V(x)being constant and nonconstant.Also,we find a possibly optimal condition on V(x).展开更多
In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome...In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome the absence of the upper semi-continuity assumption which is crucial in traditional variational methods for strongly indefinite problems.By some new tools and techniques we proved the existence of infinitely many geometrically distinct solutions if parametersλ_(1),λ_(2)>0 small enough.To the best of our knowledge,our result seems to be the first result about infinitely many solutions for Hamiltonian system involving sign-changing nonlinearity.展开更多
The degradation and nonlinear interactions of a two-breather solution of the Mel’nikov equation are analyzed.By modulating the phase shift and limit method,we prove that in different regions near the non-singular bou...The degradation and nonlinear interactions of a two-breather solution of the Mel’nikov equation are analyzed.By modulating the phase shift and limit method,we prove that in different regions near the non-singular boundaries,there are four kinds of solutions with repulsive interaction or attractive interaction in addition to the two-breather solution.They are the interaction solution between soliton and breather,the two-soliton solution,and the two-breather solution with small amplitude,which all exhibit repulsive interactions;and the two-breather solution with small amplitude,which exhibits attractive interaction.Interestingly,a new breather acts as a messenger to transfer energy during the interaction between two breather solutions with small amplitude.展开更多
In this paper,we investigate the following fractional Schrödinger-Poisson system with concave-convex nonlinearities and a steep potential well{(-Δ)^(s)u+V_(λ)(x)u+ϕu=f(x)|u|^(q-2)u+|u|^(p-2)u,in R^(3),(-Δ)^(t)...In this paper,we investigate the following fractional Schrödinger-Poisson system with concave-convex nonlinearities and a steep potential well{(-Δ)^(s)u+V_(λ)(x)u+ϕu=f(x)|u|^(q-2)u+|u|^(p-2)u,in R^(3),(-Δ)^(t)ϕ=u^(2),in R^(3),where s∈(3/4,1),t∈(0,1),q∈(1,2),p∈(4,2_(s)^(*)),2_(s)^(*):=6/3-2s is the fractional critical exponent in dimension 3,V_(λ)(x)=λV(x)+1 withλ>0.Under the case of steep potential well,we obtain the existence of the sign-changing solutions for the above system by using the constraint variational method and the quantitative deformation lemma.Furthermore,we prove that the energy of ground state sign-changing solution is strictly more than twice of the energy of the ground state solution.Our results improve the recent results in the literature.展开更多
In this paper,we study the following Schrödinger-Poisson system{-ε^(p)Δ_(p)u+V(x)|u|^(p-2)u+ϕ|u|^(p-2)u=f(u)+|u|^(p*-2)u in R^(3),-ε^(2)Δϕ=|u|^(p)in R^(3),whereε>0 is a parameter,3/2<p<3,Δ_(p)u=div...In this paper,we study the following Schrödinger-Poisson system{-ε^(p)Δ_(p)u+V(x)|u|^(p-2)u+ϕ|u|^(p-2)u=f(u)+|u|^(p*-2)u in R^(3),-ε^(2)Δϕ=|u|^(p)in R^(3),whereε>0 is a parameter,3/2<p<3,Δ_(p)u=div(|∇u|^(p-2)∇u),p^(*)=3p/3-p,V:R^(3)→R is a potential function with a local minimum and f is subcritical growth.Based on the penalization method,Nehari manifold techniques and Ljusternik-Schnirelmann category theory,we obtain the multiplicity and concentration of positive solutions to the above system.展开更多
In this paper,we consider the p-Laplacian Schrödinger-Poisson equation with L^(2)-norm constraint-Δ_(p)u+|u|^(p-2)u+λu+(1/4π|x|*|u|^(2))u=|u|^(q-2)u,x∈R^(3),where 2≤p<3,5p/3<q<p*=3p/3-p,λ>0 is a...In this paper,we consider the p-Laplacian Schrödinger-Poisson equation with L^(2)-norm constraint-Δ_(p)u+|u|^(p-2)u+λu+(1/4π|x|*|u|^(2))u=|u|^(q-2)u,x∈R^(3),where 2≤p<3,5p/3<q<p*=3p/3-p,λ>0 is a Lagrange multiplier.We obtain the critical point of the corresponding functional of the problem on mass constraint by the variational method and the Mountain pass lemma,and then find a normalized solution to this equation.展开更多
This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution ...This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.展开更多
In this paper,we study the self-similar solutions of the degenerate diffusion equation ut-div(|▽u^(m)|^(p-2)▽u^(m))=0 of polytropic filtration diffusion in R^(N)×(0,±∞)or(R^(N)/{0})×(0,±∞)with ...In this paper,we study the self-similar solutions of the degenerate diffusion equation ut-div(|▽u^(m)|^(p-2)▽u^(m))=0 of polytropic filtration diffusion in R^(N)×(0,±∞)or(R^(N)/{0})×(0,±∞)with N≥1,m>0,p>1,such that m(p-1)>1.We give a clear classification of the self-similar solutions of the form u(x,t)=(βt)^(-α/β)((βt)^(-1/β)|x|)withα∈R andβ=α[m(p-1)-1]+p,regular or singular at the origin point.The existence and uniqueness of some solutions are established by the phase plane analysis method,and the asymptotic properties of the solutions near the origin and the infinity are also described.This paper extends the classical results of self-similar solutions for degeneratep-Laplace heat equation by Bidaut-Véron[Proc Royal Soc Edinburgh,2009,139:1-43]to the doubly nonlinear degenerate diffusion equations.展开更多
In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρ...In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.展开更多
A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions o...A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.展开更多
This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depen...This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.展开更多
This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ...This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.展开更多
In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are...In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.展开更多
Comisión Nacional de Energía Atómica (CNEA) has the responsibility for restoring uranium mining facilities once the operations have finished.CNEA,within its Environmental Program and in compliance with ...Comisión Nacional de Energía Atómica (CNEA) has the responsibility for restoring uranium mining facilities once the operations have finished.CNEA,within its Environmental Program and in compliance with its legal responsibilities,decides to implement a restoration project for all sites related to the mining and processing of uranium ores.The Malargüe Site is located within the Province of Mendoza in the city of Malargüe.It is the first site to successfully complete its remediation.The activities consist of relocation of tailings to an engineering repository.The tailings management(encapsulation) and rehabilitation of the area was finished in June 2017.The remediation alternative for the ore tailings was selected after conducting comparative studies and submitted the project to the society for consideration.The objective of the encapsulation of the mineral tails is to isolate them from the environment,also proceeding with the decontamination and rehabilitation of the area (landscaping,post-closure monitoring and 20 years monitoring period).Encapsulation consisted of the construction of a containment cell for the mine tailings,to isolate them and prevent pollutants from entering the environment through the transfer routes.To clean the impacted areas,the soil was removed,it was incorporated into the encapsulation,and the filling was carried out with natural soils from the area.Remediation prevents radon transfer to the environment,as ^(222)Ra is an alpha emitter with a half-life of four days,which produces its own radioactive progeny.Radon progeny are solids,and when a ^(222)Ra nucleus emits an alpha particle into the air,the resulting ^(218)Po nucleus,momentarily electrically charged,adheres to any dust particle.Remediation prevents the discharge into the air containing radon and also containing dust particles charged with intensely radioactive radon progeny.The tasks mentioned make it possible to decrease radon emanation,reduce radiological risks to the public and prevent the entry of rainwater into the system.In addition,the containment system prevents the discharge of contaminated liquids into the environment,avoiding contamination of the groundwater.All these activities are according to the concepts of sustainability.展开更多
This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ...This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.展开更多
Sonoluminescence is more distinctly observed in phosphoric and sulfuric acid,which exhibit high viscosity and lower vapor pressures relative to water.Within an 85-wt%phosphoric acid solution saturated with argon(Ar),v...Sonoluminescence is more distinctly observed in phosphoric and sulfuric acid,which exhibit high viscosity and lower vapor pressures relative to water.Within an 85-wt%phosphoric acid solution saturated with argon(Ar),variations in the light-emitting regimes of bubbles were noted to correspond with increments in the driving acoustic intensity.Specifically,the bubbles were observed to perform a dance-like motion 2 cm below the multi-bubble sonoluminescence(MBSL)cluster,traversing a 25-mm^(2) grid during the camera exposure period.Spectral analysis conducted at the beginning of the experiment showed a gradual attenuation of CN(B^(2)Σ–X^(2)Σ)emission concurrent with a strengthening of Ar(4p–4s)atom emission lines.The application of a theoretical temperature model to the spectral data revealed that the internal temperature of the bubbles escalates swiftly upon their implosion.This study is instrumental in advancing the comprehension of the underlying mechanisms of sonoluminescence and in the formulation of a dynamic model for the behavior of the bubbles.展开更多
We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular ma...We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular matrix.These are a kind of spatiotemporal symmetric solutions,e.g.spiral waves.We give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic solutions.The transversal condition is determined using the Brouwer degree.We also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.展开更多
We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavio...We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavior of a solution u near the boundary OD up to the third or higher term.展开更多
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12101572 and 12371256)2024 Shanxi Province Graduate Innovation Project (Grant No. 2024KY615)the Fundamental Research Program of Shanxi Province of China (Grant No. 202403021211002)。
文摘The N-periodic wave solvability problem for the N=1 supersymmetric Sawada–Kotera–Ramani equation is considered by combining the Hirota's bilinear method and the super Riemann theta function. The constraint equations and unknown parameters are redefined, and the numerical calculation process of the N-periodic wave solutions is derived. It has been verified that under certain conditions, the asymptotic relations between N-periodic wave solutions and N-soliton solutions can be established. Some numerical solutions of three-periodic wave are presented. Under the influence of the Grassmann variable, the three-periodic wave solutions will generate an influence band in the middle region, and the amplitude becomes bigger as the distance from the influence band increases.
基金supported by the NSFC(11931012,11871387,12371118)。
文摘We are concerned with a nonlinear elliptic equation,involving a Kirchhoff type nonlocal term and a potential V(x),onℝ3.As is well known that,even in,H_(r)^(1)(R^(3)),the nonlinear term is a pure power form of∣u∣^(p−1)u and V(x)≡1,it seems very difficult to apply the mountain-pass theorem to get a solution(i.e.,mountain-pass solution)to this kind of equation for all p∈(1,5),due to the difficulty of verifying the boundedness of the PalaisSmale sequence obtained by the mountain-pass theorem when p∈(1,3).In this paper,we find a new strategy to overcome this difficulty,and then get a mountain-pass solution to the equation for all p∈(1,5)and for both V(x)being constant and nonconstant.Also,we find a possibly optimal condition on V(x).
基金supported by the NSFC(11301297)the Hubei Provincial Natural Science Foundation of China(2024AFB730)+3 种基金the Yichang City Natural Science Foundation(A-24-3-008)the Open Research Fund of Key Laboratory of Nonlinear Analysis and Applications(Central China Normal University),Ministry of Education,P.R.China(NAA2024ORG003)Gu's research was supported by the Zhejiang Provincial Natural Science Foundation(LQ21A010014)the NFSC(12101577).
文摘In this paper,we study the elliptic system{-Δu+V(x)u=|v|^(p-2)v-λ_(2)|v|^(s2-2)v,-Δu+V(x)v=|u|^(p-2)u-λ_(1)|u|^(s1-2)u,u,v∈H^(1)(R^(N))with strongly indefinite structure and sign-changing nonlinearity.We overcome the absence of the upper semi-continuity assumption which is crucial in traditional variational methods for strongly indefinite problems.By some new tools and techniques we proved the existence of infinitely many geometrically distinct solutions if parametersλ_(1),λ_(2)>0 small enough.To the best of our knowledge,our result seems to be the first result about infinitely many solutions for Hamiltonian system involving sign-changing nonlinearity.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.52171251 and U21062251)Program of Science and Technology Innovation of Dalian(Grant No.2022JJ12GX036).
文摘The degradation and nonlinear interactions of a two-breather solution of the Mel’nikov equation are analyzed.By modulating the phase shift and limit method,we prove that in different regions near the non-singular boundaries,there are four kinds of solutions with repulsive interaction or attractive interaction in addition to the two-breather solution.They are the interaction solution between soliton and breather,the two-soliton solution,and the two-breather solution with small amplitude,which all exhibit repulsive interactions;and the two-breather solution with small amplitude,which exhibits attractive interaction.Interestingly,a new breather acts as a messenger to transfer energy during the interaction between two breather solutions with small amplitude.
基金supported by the Natural Science Foundation of Sichuan(No.2023NSFSC0073)。
文摘In this paper,we investigate the following fractional Schrödinger-Poisson system with concave-convex nonlinearities and a steep potential well{(-Δ)^(s)u+V_(λ)(x)u+ϕu=f(x)|u|^(q-2)u+|u|^(p-2)u,in R^(3),(-Δ)^(t)ϕ=u^(2),in R^(3),where s∈(3/4,1),t∈(0,1),q∈(1,2),p∈(4,2_(s)^(*)),2_(s)^(*):=6/3-2s is the fractional critical exponent in dimension 3,V_(λ)(x)=λV(x)+1 withλ>0.Under the case of steep potential well,we obtain the existence of the sign-changing solutions for the above system by using the constraint variational method and the quantitative deformation lemma.Furthermore,we prove that the energy of ground state sign-changing solution is strictly more than twice of the energy of the ground state solution.Our results improve the recent results in the literature.
基金supported by the Natural Science Foundation of Gansu Province(No.24JRRP001)。
文摘In this paper,we study the following Schrödinger-Poisson system{-ε^(p)Δ_(p)u+V(x)|u|^(p-2)u+ϕ|u|^(p-2)u=f(u)+|u|^(p*-2)u in R^(3),-ε^(2)Δϕ=|u|^(p)in R^(3),whereε>0 is a parameter,3/2<p<3,Δ_(p)u=div(|∇u|^(p-2)∇u),p^(*)=3p/3-p,V:R^(3)→R is a potential function with a local minimum and f is subcritical growth.Based on the penalization method,Nehari manifold techniques and Ljusternik-Schnirelmann category theory,we obtain the multiplicity and concentration of positive solutions to the above system.
基金supported by the National Natural Science Foundation of China(No.12461024)the Natural Science Research Project of Department of Education of Guizhou Province(Nos.QJJ2023012,QJJ2023061,QJJ2023062)the Natural Science Research Project of Guizhou Minzu University(No.GZMUZK[2022]YB06)。
文摘In this paper,we consider the p-Laplacian Schrödinger-Poisson equation with L^(2)-norm constraint-Δ_(p)u+|u|^(p-2)u+λu+(1/4π|x|*|u|^(2))u=|u|^(q-2)u,x∈R^(3),where 2≤p<3,5p/3<q<p*=3p/3-p,λ>0 is a Lagrange multiplier.We obtain the critical point of the corresponding functional of the problem on mass constraint by the variational method and the Mountain pass lemma,and then find a normalized solution to this equation.
基金supported by the Anhui Provincial Natural Science Foundation(2408085QA031)the third author's work was supported by the National Natural Science Foundation of China(12001033).
文摘This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.
基金supported by the NSFC(12271178,12171166)the Guangzhou Basic and Applied Basic Research Foundation(2024A04J2022)the TCL Young Scholar(2024-2027).
文摘In this paper,we study the self-similar solutions of the degenerate diffusion equation ut-div(|▽u^(m)|^(p-2)▽u^(m))=0 of polytropic filtration diffusion in R^(N)×(0,±∞)or(R^(N)/{0})×(0,±∞)with N≥1,m>0,p>1,such that m(p-1)>1.We give a clear classification of the self-similar solutions of the form u(x,t)=(βt)^(-α/β)((βt)^(-1/β)|x|)withα∈R andβ=α[m(p-1)-1]+p,regular or singular at the origin point.The existence and uniqueness of some solutions are established by the phase plane analysis method,and the asymptotic properties of the solutions near the origin and the infinity are also described.This paper extends the classical results of self-similar solutions for degeneratep-Laplace heat equation by Bidaut-Véron[Proc Royal Soc Edinburgh,2009,139:1-43]to the doubly nonlinear degenerate diffusion equations.
基金supported by the Technological Innovation Talents in Universities and Colleges in Henan Province(No.21HASTIT025)the Natural Science Foundation of Henan Province(No.222300420449)the Innovative Research Team of Henan Polytechnic University(No.T2022-7)。
文摘In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12261064 and 11861048)the Natural Science Foundation of Inner Mongolia,China (Grant Nos.2021MS01004 and 2022QN01008)the High-level Talents Scientific Research Start-up Foundation of Inner Mongolia University (Grant No.10000-21311201/165)。
文摘A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.
基金supported by the Key Project of the NSFC(12131010)the NSFC(11771155,12271032)+1 种基金the NSF of Guangdong Province(2021A1515010249,2021A1515010303)supported by the NSFC(11971179,12371205)。
文摘This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12275172 and 11905124)。
文摘This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.
基金supported by the NSFC (12071438)supported by the NSFC (12201232)
文摘In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.
文摘Comisión Nacional de Energía Atómica (CNEA) has the responsibility for restoring uranium mining facilities once the operations have finished.CNEA,within its Environmental Program and in compliance with its legal responsibilities,decides to implement a restoration project for all sites related to the mining and processing of uranium ores.The Malargüe Site is located within the Province of Mendoza in the city of Malargüe.It is the first site to successfully complete its remediation.The activities consist of relocation of tailings to an engineering repository.The tailings management(encapsulation) and rehabilitation of the area was finished in June 2017.The remediation alternative for the ore tailings was selected after conducting comparative studies and submitted the project to the society for consideration.The objective of the encapsulation of the mineral tails is to isolate them from the environment,also proceeding with the decontamination and rehabilitation of the area (landscaping,post-closure monitoring and 20 years monitoring period).Encapsulation consisted of the construction of a containment cell for the mine tailings,to isolate them and prevent pollutants from entering the environment through the transfer routes.To clean the impacted areas,the soil was removed,it was incorporated into the encapsulation,and the filling was carried out with natural soils from the area.Remediation prevents radon transfer to the environment,as ^(222)Ra is an alpha emitter with a half-life of four days,which produces its own radioactive progeny.Radon progeny are solids,and when a ^(222)Ra nucleus emits an alpha particle into the air,the resulting ^(218)Po nucleus,momentarily electrically charged,adheres to any dust particle.Remediation prevents the discharge into the air containing radon and also containing dust particles charged with intensely radioactive radon progeny.The tasks mentioned make it possible to decrease radon emanation,reduce radiological risks to the public and prevent the entry of rainwater into the system.In addition,the containment system prevents the discharge of contaminated liquids into the environment,avoiding contamination of the groundwater.All these activities are according to the concepts of sustainability.
基金supported by the National Natural Science Foundation of China(12301251,12271232)the Natural Science Foundation of Shandong Province,China(ZR2021QA038)the Scientific Research Foundation of Linyi University,China(LYDX2020BS014)。
文摘This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.
基金Project supported by the Scientific Research Project of Higher Education in the Inner Mongolia Autonomous Region,China(Grant No.NJZY23100)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2024FX30)the 14th Five Year Plan Project for Education Science in Inner Mongolia Autonomous Region,China(Grant No.NGJGH2023205).
文摘Sonoluminescence is more distinctly observed in phosphoric and sulfuric acid,which exhibit high viscosity and lower vapor pressures relative to water.Within an 85-wt%phosphoric acid solution saturated with argon(Ar),variations in the light-emitting regimes of bubbles were noted to correspond with increments in the driving acoustic intensity.Specifically,the bubbles were observed to perform a dance-like motion 2 cm below the multi-bubble sonoluminescence(MBSL)cluster,traversing a 25-mm^(2) grid during the camera exposure period.Spectral analysis conducted at the beginning of the experiment showed a gradual attenuation of CN(B^(2)Σ–X^(2)Σ)emission concurrent with a strengthening of Ar(4p–4s)atom emission lines.The application of a theoretical temperature model to the spectral data revealed that the internal temperature of the bubbles escalates swiftly upon their implosion.This study is instrumental in advancing the comprehension of the underlying mechanisms of sonoluminescence and in the formulation of a dynamic model for the behavior of the bubbles.
基金supported by the National Natural Science Foundation of China(1237119112071175)+4 种基金supported by the NSFC(1207117511901080)supported by the NSFC(12071175)the Fundamental Research Funds For the Central Universities(2412023YQ003)the Natural Science Foundation of Jilin Province(20200201253JC)。
文摘We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular matrix.These are a kind of spatiotemporal symmetric solutions,e.g.spiral waves.We give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic solutions.The transversal condition is determined using the Brouwer degree.We also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.
基金supported by the JSPS KAKENHI(JP22K03386)supported by the JST SPRING(JPMJSP2132)。
文摘We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavior of a solution u near the boundary OD up to the third or higher term.
