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
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
Based on a new bilinear equation,we investigated some new dynamic behaviors of the(2+1)-dimensional shallow water wave model,such as hybridization behavior between different solitons,trajectory equations for lump coll...Based on a new bilinear equation,we investigated some new dynamic behaviors of the(2+1)-dimensional shallow water wave model,such as hybridization behavior between different solitons,trajectory equations for lump collisions,and evolution behavior of multi-breathers.Firstly,the N-soliton solution of Ito equation is studied,and some high-order breather waves can be obtained from the N-soliton solutions through paired-complexification of parameters.Secondly,the high-order lump solutions and the hybrid solutions are obtained by employing the long-wave limit method,and the motion velocity and trajectory equations of high-order lump waves are analyzed.Moreover,based on the trajectory equations of the higher-order lump solutions,we give and prove the trajectory theorem of 1-lump before and after interaction with nsoliton.Finally,we obtain some new lump solutions from the multi-solitons by constructing a new test function and using the parameter limit method.Meanwhile,some evolutionary behaviors of the obtained solutions are shown through a large number of three-dimensional graphs with different and appropriate parameters.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 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 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
We investigate the radial symmetry of minimizers on the Pohozaev-Nehari manifold to the Schrodinger Poisson equation with a general nonlinearity f(u).Particularly,we allow that f is L^(2) supercritical.The main result...We investigate the radial symmetry of minimizers on the Pohozaev-Nehari manifold to the Schrodinger Poisson equation with a general nonlinearity f(u).Particularly,we allow that f is L^(2) supercritical.The main result shows that minimizers are radially symmetric modulo suitable translations.展开更多
The third-order flow Gerdjikov–Ivanov(TOFGI)equation is studied,and the Darboux transformation(DT)is used to obtain the determinant expression of the solution of this equation.On this basis,the soliton solution,ratio...The third-order flow Gerdjikov–Ivanov(TOFGI)equation is studied,and the Darboux transformation(DT)is used to obtain the determinant expression of the solution of this equation.On this basis,the soliton solution,rational solution,positon solution,and breather solution of the TOFGI equation are obtained by taking zero seed solution and non-zero seed solution.The exact solutions and dynamic properties of the Gerdjikov–Ivanov(GI)equation and the TOFGI equation are compared in detail under the same conditions,and it is found that there are some differences in the velocities and trajectories of the solutions of the two equations.展开更多
In this paper we investigate the existence of solution for the following nonlocal problem with Stein-Weiss convolution term-△Φu+V(x)Φ(|u|)u=1/|x|α(∫R^(N)K(y)F(u(y))/|x-y|Y(λ)|y|^(α)dy)K(x)f(u(x)),x∈R^(N),wher...In this paper we investigate the existence of solution for the following nonlocal problem with Stein-Weiss convolution term-△Φu+V(x)Φ(|u|)u=1/|x|α(∫R^(N)K(y)F(u(y))/|x-y|Y(λ)|y|^(α)dy)K(x)f(u(x)),x∈R^(N),where a≥0,N≥2,λ>0 is a positive parameter,V,K∈C(R^(N),[0,∞))are nonne-gative functions that may vanish at infinity,the function f E C(R,R)is quasicritical and F(t)=∫_(0)^(t)f(s)ds.To establish our existence and regularity results,we use the Hardy-type inequalities for Orlicz-Sobolev Space and the Stein-Weiss inequality together with a varia-tional technique based on the mountain pass theorem for a functional that is not necessarily in C'.Furthermore,we also prove the existence of a ground state solution by the method of Nehari manifold in the case where the strict monotonicity condition on f is not required.This work incorporates the case where the N-functionΦdoes not verify the△_(2)-condition.展开更多
In the study of the extremal for Sobolev inequality on the Heisenberg group and the Cauchy-Riemann(CR)Yamabe problem,Jerison-Lee found a three-dimensional family of differential identities for critical exponent subell...In the study of the extremal for Sobolev inequality on the Heisenberg group and the Cauchy-Riemann(CR)Yamabe problem,Jerison-Lee found a three-dimensional family of differential identities for critical exponent subelliptic equation on Heisenberg groupℍn by using the computer in[5].They wanted to know whether there is a theoretical framework that would predict the existence and the structure of such formulae.With the help of dimension conservation and invariant tensors,we can answer the above question.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
Detonation performance is crucial for evaluating the power of high explosives(HEs),and the equation of state(EOS)that accurately describes the high-temperature,high-pressure,and high-temperature,medium-pressure states...Detonation performance is crucial for evaluating the power of high explosives(HEs),and the equation of state(EOS)that accurately describes the high-temperature,high-pressure,and high-temperature,medium-pressure states of detonation products is key to assessing the damage efficiency of these energetic materials.This article examines the limitations of the VLW EOS in representing the thermodynamic states of explosive detonation gas products under high-temperature and medium-to high-pressure conditions.A new gas EOS for detonation products,called VHL(Virial-Han-Long),is proposed.The accuracy of VHL in describing gas states under high-temperature and medium-to high-pressure conditions is verified,and its performance in evaluating explosive detonation and working capabilities is explored.The results demonstrate that VHL exhibits high precision in calculating detonation performance.Subsequently,the detonation performance of three new HEs(ICM-101,ONC,and TNAZ)was calculated and compared to traditional HEs(TATB,CL-20,and HMX).The results indicate that ONC has superior detonation performance compared to the other explosives,while ICM-101 shows a detonation velocity similar to CL-20 but with slightly lower detonation pressure.The detonation characteristics of TNAZ are comparable to those of the standard HE HMX.From the perspective of products,considering the comprehensive work performance(mechanical work and detonation heat),both ONC and ICM-101demonstrate relatively superior performance.展开更多
This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽...This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.展开更多
Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided.Based...Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided.Based on these bilinear equations, some exact solutions to the three modified equations are derived.展开更多
In this study,new particle and energy balance equations have been developed to predict the electron temperature and density in locally bounded plasmas.Classical particle and energy balance equations assume that all pl...In this study,new particle and energy balance equations have been developed to predict the electron temperature and density in locally bounded plasmas.Classical particle and energy balance equations assume that all plasma within a reactor is completely confined only by the reactor walls.However,in industrial plasma reactors for semiconductor manufacturing,the plasma is partially confined by internal reactor structures.We predict the effect of the open boundary area(A′_(L,eff))and ion escape velocity(u_(i))on electron temperature and density by developing new particle and energy balance equations.Theoretically,we found a low ion escape velocity(u_(i)/u_(B)≈0.2)and high open boundary area(A′_(L,eff)/A_(T,eff)≈0.6)to result in an approximately 38%increase in electron density and an 8%decrease in electron temperature compared to values in a fully bounded reactor.Additionally,we suggest that the velocity of ions passing through the open boundary should exceedω_(pi)λ_(De)under the condition E^(2)_(0)?(Φ/λ_(De))^(2).展开更多
By the modifying loss function MSE and training area of physics-informed neural networks(PINNs),we propose a neural networks model,namely prior-information PINNs(PIPINNs).We demonstrate the advantages of PIPINNs by si...By the modifying loss function MSE and training area of physics-informed neural networks(PINNs),we propose a neural networks model,namely prior-information PINNs(PIPINNs).We demonstrate the advantages of PIPINNs by simulating Ai-and Bi-soliton solutions of the cylindrical Korteweg-de Vries(cKdV)equation.展开更多
This paper is devoted to understanding the stability of perturbations around the hydrostatic equilibrium of the Boussinesq system in order to gain insight into certain atmospheric and oceanographic phenomena.The Bouss...This paper is devoted to understanding the stability of perturbations around the hydrostatic equilibrium of the Boussinesq system in order to gain insight into certain atmospheric and oceanographic phenomena.The Boussinesq system focused on here is anisotropic,and involves only horizontal dissipation and thermal damping.In the 2D case R^(2),due to the lack of vertical dissipation,the stability and large-time behavior problems have remained open in a Sobolev setting.For the spatial domain T×R,this paper solves the stability problem and gives the precise large-time behavior of the perturbation.By decomposing the velocity u and temperatureθinto the horizontal average(ū,θ)and the corresponding oscillation(ū,θ),we can derive the global stability in H~2 and the exponential decay of(ū,θ)to zero in H^(1).Moreover,we also obtain that(ū_(2),θ)decays exponentially to zero in H^(1),and thatū_(1)decays exponentially toū_(1)(∞)in H^(1)as well;this reflects a strongly stratified phenomenon of buoyancy-driven fluids.In addition,we establish the global stability in H^(3)for the 3D case R^(3).展开更多
In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation e...In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.展开更多
The COVID-19 outbreak has significantly disrupted the lives of individuals worldwide.Following the lifting of COVID-19 interventions,there is a heightened risk of future outbreaks from other circulating respiratory in...The COVID-19 outbreak has significantly disrupted the lives of individuals worldwide.Following the lifting of COVID-19 interventions,there is a heightened risk of future outbreaks from other circulating respiratory infections,such as influenza-like illness(ILI).Accurate prediction models for ILI cases are crucial in enabling governments to implement necessary measures and persuade individuals to adopt personal precautions against the disease.This paper aims to provide a forecasting model for ILI cases with actual cases.We propose a specific model utilizing the partial differential equation(PDE)that will be developed and validated using real-world data obtained from the Chinese National Influenza Center.Our model combines the effects of transboundary spread among regions in China mainland and human activities’impact on ILI transmission dynamics.The simulated results demonstrate that our model achieves excellent predictive performance.Additionally,relevant factors influencing the dissemination are further examined in our analysis.Furthermore,we investigate the effectiveness of travel restrictions on ILI cases.Results can be used to utilize to mitigate the spread of disease.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Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
基金Project supported by the National Natural Science Foundation of China(Grant No.12461047)the Scientific Research Project of the Hunan Education Department(Grant No.24B0478).
文摘Based on a new bilinear equation,we investigated some new dynamic behaviors of the(2+1)-dimensional shallow water wave model,such as hybridization behavior between different solitons,trajectory equations for lump collisions,and evolution behavior of multi-breathers.Firstly,the N-soliton solution of Ito equation is studied,and some high-order breather waves can be obtained from the N-soliton solutions through paired-complexification of parameters.Secondly,the high-order lump solutions and the hybrid solutions are obtained by employing the long-wave limit method,and the motion velocity and trajectory equations of high-order lump waves are analyzed.Moreover,based on the trajectory equations of the higher-order lump solutions,we give and prove the trajectory theorem of 1-lump before and after interaction with nsoliton.Finally,we obtain some new lump solutions from the multi-solitons by constructing a new test function and using the parameter limit method.Meanwhile,some evolutionary behaviors of the obtained solutions are shown through a large number of three-dimensional graphs with different and appropriate parameters.
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(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 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 NSFC(12031015)Song's research was supported by the Shuimu Tsinghua Scholar Program,the National Funded Postdoctoral Research Program(GZB20230368)the China Postdoctoral Science Foundation(2024T170452)。
文摘We investigate the radial symmetry of minimizers on the Pohozaev-Nehari manifold to the Schrodinger Poisson equation with a general nonlinearity f(u).Particularly,we allow that f is L^(2) supercritical.The main result shows that minimizers are radially symmetric modulo suitable translations.
基金Project supported by the National Natural Science Foundation of China(Grant No.12201329)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY24A010002)the Natural Science Foundation of Ningbo(Grant No.2023J126)。
文摘The third-order flow Gerdjikov–Ivanov(TOFGI)equation is studied,and the Darboux transformation(DT)is used to obtain the determinant expression of the solution of this equation.On this basis,the soliton solution,rational solution,positon solution,and breather solution of the TOFGI equation are obtained by taking zero seed solution and non-zero seed solution.The exact solutions and dynamic properties of the Gerdjikov–Ivanov(GI)equation and the TOFGI equation are compared in detail under the same conditions,and it is found that there are some differences in the velocities and trajectories of the solutions of the two equations.
基金supported by FAPESQ/Brazil(Grant No.3031/2021)supported by CNPq/Brazil(Grant No.309.692/2020-2)and FAPESQ/Brazil(Grant No.3031/2021).
文摘In this paper we investigate the existence of solution for the following nonlocal problem with Stein-Weiss convolution term-△Φu+V(x)Φ(|u|)u=1/|x|α(∫R^(N)K(y)F(u(y))/|x-y|Y(λ)|y|^(α)dy)K(x)f(u(x)),x∈R^(N),where a≥0,N≥2,λ>0 is a positive parameter,V,K∈C(R^(N),[0,∞))are nonne-gative functions that may vanish at infinity,the function f E C(R,R)is quasicritical and F(t)=∫_(0)^(t)f(s)ds.To establish our existence and regularity results,we use the Hardy-type inequalities for Orlicz-Sobolev Space and the Stein-Weiss inequality together with a varia-tional technique based on the mountain pass theorem for a functional that is not necessarily in C'.Furthermore,we also prove the existence of a ground state solution by the method of Nehari manifold in the case where the strict monotonicity condition on f is not required.This work incorporates the case where the N-functionΦdoes not verify the△_(2)-condition.
基金supported by the National Natural Science Foundation of China(12141105,12471194)the first author’s research also was supported by the National Key Research and Development Project(SQ2020YFA070080).
文摘In the study of the extremal for Sobolev inequality on the Heisenberg group and the Cauchy-Riemann(CR)Yamabe problem,Jerison-Lee found a three-dimensional family of differential identities for critical exponent subelliptic equation on Heisenberg groupℍn by using the computer in[5].They wanted to know whether there is a theoretical framework that would predict the existence and the structure of such formulae.With the help of dimension conservation and invariant tensors,we can answer the above question.
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 National Natural Science Foundation of China(Gant Nos.11372291 and 11902298)。
文摘Detonation performance is crucial for evaluating the power of high explosives(HEs),and the equation of state(EOS)that accurately describes the high-temperature,high-pressure,and high-temperature,medium-pressure states of detonation products is key to assessing the damage efficiency of these energetic materials.This article examines the limitations of the VLW EOS in representing the thermodynamic states of explosive detonation gas products under high-temperature and medium-to high-pressure conditions.A new gas EOS for detonation products,called VHL(Virial-Han-Long),is proposed.The accuracy of VHL in describing gas states under high-temperature and medium-to high-pressure conditions is verified,and its performance in evaluating explosive detonation and working capabilities is explored.The results demonstrate that VHL exhibits high precision in calculating detonation performance.Subsequently,the detonation performance of three new HEs(ICM-101,ONC,and TNAZ)was calculated and compared to traditional HEs(TATB,CL-20,and HMX).The results indicate that ONC has superior detonation performance compared to the other explosives,while ICM-101 shows a detonation velocity similar to CL-20 but with slightly lower detonation pressure.The detonation characteristics of TNAZ are comparable to those of the standard HE HMX.From the perspective of products,considering the comprehensive work performance(mechanical work and detonation heat),both ONC and ICM-101demonstrate relatively superior performance.
基金supported by the National Natural Science Foundation of China(12271296,12271195).
文摘This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11931017 and 12071447)。
文摘Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided.Based on these bilinear equations, some exact solutions to the three modified equations are derived.
文摘In this study,new particle and energy balance equations have been developed to predict the electron temperature and density in locally bounded plasmas.Classical particle and energy balance equations assume that all plasma within a reactor is completely confined only by the reactor walls.However,in industrial plasma reactors for semiconductor manufacturing,the plasma is partially confined by internal reactor structures.We predict the effect of the open boundary area(A′_(L,eff))and ion escape velocity(u_(i))on electron temperature and density by developing new particle and energy balance equations.Theoretically,we found a low ion escape velocity(u_(i)/u_(B)≈0.2)and high open boundary area(A′_(L,eff)/A_(T,eff)≈0.6)to result in an approximately 38%increase in electron density and an 8%decrease in electron temperature compared to values in a fully bounded reactor.Additionally,we suggest that the velocity of ions passing through the open boundary should exceedω_(pi)λ_(De)under the condition E^(2)_(0)?(Φ/λ_(De))^(2).
基金supported by the National Natural Science Foundation of China(Grant Nos.12175111 and 12235007)the K.C.Wong Magna Fund in Ningbo University。
文摘By the modifying loss function MSE and training area of physics-informed neural networks(PINNs),we propose a neural networks model,namely prior-information PINNs(PIPINNs).We demonstrate the advantages of PIPINNs by simulating Ai-and Bi-soliton solutions of the cylindrical Korteweg-de Vries(cKdV)equation.
基金supported by National Natural Science Foundation of China(12071391,12231016)the Guangdong Basic and Applied Basic Research Foundation(2022A1515010860)。
文摘This paper is devoted to understanding the stability of perturbations around the hydrostatic equilibrium of the Boussinesq system in order to gain insight into certain atmospheric and oceanographic phenomena.The Boussinesq system focused on here is anisotropic,and involves only horizontal dissipation and thermal damping.In the 2D case R^(2),due to the lack of vertical dissipation,the stability and large-time behavior problems have remained open in a Sobolev setting.For the spatial domain T×R,this paper solves the stability problem and gives the precise large-time behavior of the perturbation.By decomposing the velocity u and temperatureθinto the horizontal average(ū,θ)and the corresponding oscillation(ū,θ),we can derive the global stability in H~2 and the exponential decay of(ū,θ)to zero in H^(1).Moreover,we also obtain that(ū_(2),θ)decays exponentially to zero in H^(1),and thatū_(1)decays exponentially toū_(1)(∞)in H^(1)as well;this reflects a strongly stratified phenomenon of buoyancy-driven fluids.In addition,we establish the global stability in H^(3)for the 3D case R^(3).
基金supported by the NSFC(12101012)the PhD Scientific Research Start-up Foundation of Anhui Normal University.Zeng’s research was supported by the NSFC(11961160716,11871054,12131017).
文摘In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.
基金supported by the National Natural Science Foundation of China(Grant No.62373197)Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX18_0892).
文摘The COVID-19 outbreak has significantly disrupted the lives of individuals worldwide.Following the lifting of COVID-19 interventions,there is a heightened risk of future outbreaks from other circulating respiratory infections,such as influenza-like illness(ILI).Accurate prediction models for ILI cases are crucial in enabling governments to implement necessary measures and persuade individuals to adopt personal precautions against the disease.This paper aims to provide a forecasting model for ILI cases with actual cases.We propose a specific model utilizing the partial differential equation(PDE)that will be developed and validated using real-world data obtained from the Chinese National Influenza Center.Our model combines the effects of transboundary spread among regions in China mainland and human activities’impact on ILI transmission dynamics.The simulated results demonstrate that our model achieves excellent predictive performance.Additionally,relevant factors influencing the dissemination are further examined in our analysis.Furthermore,we investigate the effectiveness of travel restrictions on ILI cases.Results can be used to utilize to mitigate the spread of disease.
