The thermistor problem is a coupled system of nonlinear PDEs with mixed boundary conditions. The goal of this paper is to study the existence, boundedness and uniqueness of the weak solution for this problem.
In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existenc...In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.展开更多
We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system.Under the conditions of slight density and te...We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system.Under the conditions of slight density and temperature variations,we verify that the full compressible Navier-Stokes-Korteweg equations admit a unique strong solution as long as the solution of the limiting system exists,when the Mach number is sufficiently small.Furthermore,we deduce the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on the time interval in which the solution exists.展开更多
Ealstence and regularity of steady state solutions to the basic semiconductor equations with the non-monotone net recombination rate are proved. A sufficient condition for the uniqueness of the steady state solutions ...Ealstence and regularity of steady state solutions to the basic semiconductor equations with the non-monotone net recombination rate are proved. A sufficient condition for the uniqueness of the steady state solutions is given. The uniqueness result is very general which contains almost all known conclusions.展开更多
In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum...In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum is allowed.展开更多
In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate cri...In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.展开更多
We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the k...We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.展开更多
We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global min...We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.展开更多
By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result o...By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.展开更多
In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equatio...In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equation, and then by a priori estimates method, we extend the local solution to a global solution.展开更多
In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existen...By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.展开更多
In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases ...In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified SchrSdinger equations.展开更多
In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.
The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type ...The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.展开更多
1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2（O, +∞） into Lt2q（O, ∞）, v>2. When v=N-1...1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2（O, +∞） into Lt2q（O, ∞）, v>2. When v=N-1 we can get the radial solutions of problem where 2*=2N/N-2 is the critical exponent of the Sobolev embedding H1（Rn）→LQ（RN）. Kurtz has discussed the existence of κ-node solution of （1.1）, （1.2） for each κ∈N U{0} when the growth rate of |u|l-1u+f（u） is lower then |u|v+3/v-1 i.e.展开更多
This paper deals with an abstract periodic gradient system in which the gradient is taken with respect to a variable metric. We obtain an existence and uniqueness result via the application of a global inverse theorem.
In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations ut -Dj （α^ij （x, t, u）Diψ（u）） ＋b^i （t, u）Diu＋C（x, t, u） = 0, and obtain the existence, un...In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations ut -Dj （α^ij （x, t, u）Diψ（u）） ＋b^i （t, u）Diu＋C（x, t, u） = 0, and obtain the existence, uniqueness and blow-up in finite time of these solutions under some structure conditions.展开更多
文摘The thermistor problem is a coupled system of nonlinear PDEs with mixed boundary conditions. The goal of this paper is to study the existence, boundedness and uniqueness of the weak solution for this problem.
基金supported by Natural Science Foundation of China(11771166)Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT 17R46financially supported by funding for basic research business in Central Universities(innovative funding projects)(2018CXZZ090)。
文摘In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.
文摘We investigate the long time existence of strong solutions to the initial value problem for the three-dimensional non-isentropic compressible Navier-Stokes-Korteweg system.Under the conditions of slight density and temperature variations,we verify that the full compressible Navier-Stokes-Korteweg equations admit a unique strong solution as long as the solution of the limiting system exists,when the Mach number is sufficiently small.Furthermore,we deduce the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on the time interval in which the solution exists.
文摘Ealstence and regularity of steady state solutions to the basic semiconductor equations with the non-monotone net recombination rate are proved. A sufficient condition for the uniqueness of the steady state solutions is given. The uniqueness result is very general which contains almost all known conclusions.
基金partially supported by the National Natural Science Foundation of China (11671273 and 11931010)key research project of the Academy for Multidisciplinary Studies of CNU and Beijing Natural Science Foundation (1192001).
文摘In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum is allowed.
基金supported by the Natural Science Foundation of China(11771166,12071169)the Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT17R46。
文摘In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.
基金supported by the National Natural Science Foundation of China (12001033)。
文摘We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.
文摘We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.
文摘By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.
文摘In this paper, we establish the global existence of the solution for the Landau-Lifshitz equation of the ferromagnetic spin chain. By Galerkin method, we first show the existence of the local solution for this equation, and then by a priori estimates method, we extend the local solution to a global solution.
文摘In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
基金supported by Scientific Research Fund of Heilongjiang Provincial Education Department (11544032)the National Natural Science Foundation of China (10571021, 10701020)
文摘By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.
基金supported by JSPS Grant-in-Aid for Scientific Research(C)(15K04970)
文摘In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified SchrSdinger equations.
基金supported by the National Natural Science Foundation of China（11371027） the Projects of Outstanding Young Talents of Universities in Anhui Province（gxyq2018116）+2 种基金 the Teaching Groups in Anhui Province（2016jxtd080,2015jxtd048） the NSF of Educational Bureau of Anhui Province（KJ2017A702,KJ2017A704） the NSF of Bozhou University（BZSZKYXM201302,BSKY201539）
文摘In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.
文摘The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.
文摘1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2（O, +∞） into Lt2q（O, ∞）, v>2. When v=N-1 we can get the radial solutions of problem where 2*=2N/N-2 is the critical exponent of the Sobolev embedding H1（Rn）→LQ（RN）. Kurtz has discussed the existence of κ-node solution of （1.1）, （1.2） for each κ∈N U{0} when the growth rate of |u|l-1u+f（u） is lower then |u|v+3/v-1 i.e.
文摘This paper deals with an abstract periodic gradient system in which the gradient is taken with respect to a variable metric. We obtain an existence and uniqueness result via the application of a global inverse theorem.
基金Foundation item： Supported by National Science Foundation of China（10572156） Supported by Natural Science Foundation of Henan Province（0211010900） Supported by National Science Foundation of Department of Education of Henan Province（200510465001）
文摘In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations ut -Dj （α^ij （x, t, u）Diψ（u）） ＋b^i （t, u）Diu＋C（x, t, u） = 0, and obtain the existence, uniqueness and blow-up in finite time of these solutions under some structure conditions.
