This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source,subject to the null Dirichlet boundary condition.We first give sufficient conditi...This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source,subject to the null Dirichlet boundary condition.We first give sufficient conditions for that the solution exists globally or blows up in the finite time.Then the blow-up time is also given.At last,we obtain a property differing from the local source which the blow-up set is the entire interval.展开更多
This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient ...This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient conditions for the global existence of solution are obtained.展开更多
The author considers the Klien-Gordon equations utt --△u+μu= f(u) (P >0, |f(u)| ≤ c|u|α+1 ). The necessary and sufficient condition of existence of global solutions is obtained for f(s)dsdx <d (d is the give...The author considers the Klien-Gordon equations utt --△u+μu= f(u) (P >0, |f(u)| ≤ c|u|α+1 ). The necessary and sufficient condition of existence of global solutions is obtained for f(s)dsdx <d (d is the given constant).展开更多
The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that t...The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that the asymptotic profile of the solution is quite different from that of the free solution.展开更多
In this paper, we prove the global existence and uniqueness of non-negative classical solutions of the Smoluchowski equation with viscosity ε>0. The existence of weak solutions when ε=0 is also obtained.
基金Supported by the National Natural Science Foundation of China（10571024）
文摘This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source,subject to the null Dirichlet boundary condition.We first give sufficient conditions for that the solution exists globally or blows up in the finite time.Then the blow-up time is also given.At last,we obtain a property differing from the local source which the blow-up set is the entire interval.
文摘This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient conditions for the global existence of solution are obtained.
文摘The author considers the Klien-Gordon equations utt --△u+μu= f(u) (P >0, |f(u)| ≤ c|u|α+1 ). The necessary and sufficient condition of existence of global solutions is obtained for f(s)dsdx <d (d is the given constant).
基金Project supported by the National Natural Science Foundation of China (No.10271108).
文摘The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that the asymptotic profile of the solution is quite different from that of the free solution.
基金This research is supported by the National Natural Science Foundation of China
文摘In this paper, we prove the global existence and uniqueness of non-negative classical solutions of the Smoluchowski equation with viscosity ε>0. The existence of weak solutions when ε=0 is also obtained.
