In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solu...In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.展开更多
In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx...In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.展开更多
In this paper, we study the asymptotic behavior of globally smooth solutions of initial boundary value problem for 1-d quasineutral drift-diffusion model for semiconductors. We prove that the smooth solutions（close t...In this paper, we study the asymptotic behavior of globally smooth solutions of initial boundary value problem for 1-d quasineutral drift-diffusion model for semiconductors. We prove that the smooth solutions（close to equilibrium）of the problem converge to the unique stationary solution.展开更多
The authors study a generalized thin film equation. Under some assumptions on the initial value, the existence of weak solutions is established by the time-discrete method.The uniqueness and asymptotic behavior of sol...The authors study a generalized thin film equation. Under some assumptions on the initial value, the existence of weak solutions is established by the time-discrete method.The uniqueness and asymptotic behavior of solutions are also discussed.展开更多
This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ i...This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ in the energy norm, and to show it has a free profile as t →＋∞. Our approach is based on the work of [11]. Namely we use a weighted L^∞ norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper.展开更多
The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in s...The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in some cases asymptotic behaviour.展开更多
We consider the quasilinear Schrdinger equations of the form-ε~2？u ＋ V（x）u- ε~2？（u2）u = g（u）, x ∈ R^N,where ε 〉 0 is a small parameter, the nonlinearity g（u） ∈ C^1（R） is an odd function with subcrit...We consider the quasilinear Schrdinger equations of the form-ε~2？u ＋ V（x）u- ε~2？（u2）u = g（u）, x ∈ R^N,where ε 〉 0 is a small parameter, the nonlinearity g（u） ∈ C^1（R） is an odd function with subcritical growth and V（x） is a positive Hlder continuous function which is bounded from below, away from zero, and infΛV（x） 0 such that for all ε∈（0, ε0],the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V（x） as ε→ 0~＋.展开更多
In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned wi...In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned with the dynamic behaviors of a delay stochastic competitive system. We first obtain the global existence of a unique positive solution of system. Later, we show that the solution of system will be stochastically ultimate boundedness. However, large noises may make the system extinct exponentially with probability one. Also, sufficient conditions for the global attractivity of system are established. FinMly, illustrated examples are given to show the effectiveness of the proposed criteria.展开更多
The initial boundary value problems (IBVP) for the system of compressible adiabatic flow through porous media and the IBVP for its corresponding reduced system through Darcy’ laws on [0, 1] x [0, +] are considered re...The initial boundary value problems (IBVP) for the system of compressible adiabatic flow through porous media and the IBVP for its corresponding reduced system through Darcy’ laws on [0, 1] x [0, +] are considered respectively. The global existence of smooth solutions to the IBVP problems for two systems are proved, and their large-time behavior is analyzed. The time-asymptotic equivalence of these two systems are investigated, the decay rate of the difference of solutions between these two systems are shown to be determined explicitly by the initial perturbations and boundary effects. It is found that the oscillation of the specific volume can be cancelled by that of entropy, i.e., the oscillation of the specific volume and entropy is not required to be small.展开更多
基金Supported by the Natural Science Foundation of Zhejiang Provivce (102009)Supported by the Natural Foundation of Huzhou Teacher's College(200302)
文摘In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.
基金Supported by the National Natural Science Foundation of China（10671182）
文摘In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.
基金Supported by the Financial Project of Key Youth in College of Henan Province
文摘In this paper, we study the asymptotic behavior of globally smooth solutions of initial boundary value problem for 1-d quasineutral drift-diffusion model for semiconductors. We prove that the smooth solutions（close to equilibrium）of the problem converge to the unique stationary solution.
基金Project supported by the 973 Project of the Ministry of Science and Technology of China and the National Natural Science Foundation of China (No.10125107)
文摘The authors study a generalized thin film equation. Under some assumptions on the initial value, the existence of weak solutions is established by the time-discrete method.The uniqueness and asymptotic behavior of solutions are also discussed.
基金Project supported by Grant-in-Aid for Science Research (No.12740105, No.14204011), JSPS.
文摘This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ in the energy norm, and to show it has a free profile as t →＋∞. Our approach is based on the work of [11]. Namely we use a weighted L^∞ norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper.
基金Project supported by the Swiss National Science Foundation under the contract#20-67618.02.
文摘The authors consider a class of nonlinear parabolic problems where the lower order term isdepending on a weighted integral of the solution, and address the issues of existence, uniqueness,stationary solutions and in some cases asymptotic behaviour.
基金supported by National Natural Science Foundation of China(Grant Nos.11371160 and 11328101)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.#IRT13066)
文摘We consider the quasilinear Schrdinger equations of the form-ε~2？u ＋ V（x）u- ε~2？（u2）u = g（u）, x ∈ R^N,where ε 〉 0 is a small parameter, the nonlinearity g（u） ∈ C^1（R） is an odd function with subcritical growth and V（x） is a positive Hlder continuous function which is bounded from below, away from zero, and infΛV（x） 0 such that for all ε∈（0, ε0],the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V（x） as ε→ 0~＋.
基金Acknowledgments The authors thank the referees for their reports and many valuable comments and suggestions that greatly improved the presentation of this paper. The work is supported by the National Natural Science Foundation of China （No. 11261017）, the Key Laboratory of Biological Resources Protection and Utilization of Hubei Province （No. PKLHB1323） and the Key Project of Chinese Ministry of Education （No. 212111）.
文摘In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned with the dynamic behaviors of a delay stochastic competitive system. We first obtain the global existence of a unique positive solution of system. Later, we show that the solution of system will be stochastically ultimate boundedness. However, large noises may make the system extinct exponentially with probability one. Also, sufficient conditions for the global attractivity of system are established. FinMly, illustrated examples are given to show the effectiveness of the proposed criteria.
基金the MST Grant #1999075107 and the Innovation funds of AMSS, CAS of China.
文摘The initial boundary value problems (IBVP) for the system of compressible adiabatic flow through porous media and the IBVP for its corresponding reduced system through Darcy’ laws on [0, 1] x [0, +] are considered respectively. The global existence of smooth solutions to the IBVP problems for two systems are proved, and their large-time behavior is analyzed. The time-asymptotic equivalence of these two systems are investigated, the decay rate of the difference of solutions between these two systems are shown to be determined explicitly by the initial perturbations and boundary effects. It is found that the oscillation of the specific volume can be cancelled by that of entropy, i.e., the oscillation of the specific volume and entropy is not required to be small.
