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
In this article,we discuss the blowup phenomenon of solutions to the wdiffusion equation with Dirichlet boundary conditions on the graph.Through Banach fixed point theorem,comparison principle,construction of auxiliar...In this article,we discuss the blowup phenomenon of solutions to the wdiffusion equation with Dirichlet boundary conditions on the graph.Through Banach fixed point theorem,comparison principle,construction of auxiliary function and other methods,we prove the local existence of solutions,and under appropriate conditions the blowup time and blowup rate estimation are given.Finally,numerical experiments are given to illustrate the blowup behavior of the solution.展开更多
A nonlinear degenerate parabolic equation with nonlocal source was considered. It was shown that under certain assumptions the solution of the equation blows up in finite time and the set of blowup points is the whole...A nonlinear degenerate parabolic equation with nonlocal source was considered. It was shown that under certain assumptions the solution of the equation blows up in finite time and the set of blowup points is the whole region. The integral method is used to investigate the blowup properties of the solution.展开更多
In this paper we consider the existence and asymptotic estimates of global solutions and finite time blowup of local solutions of quasilinear parabolic equation with critical Sobolev exponent and with lower energy ini...In this paper we consider the existence and asymptotic estimates of global solutions and finite time blowup of local solutions of quasilinear parabolic equation with critical Sobolev exponent and with lower energy initial value; we also describe the asymptotic behavior of global solutions with high energy initial value.展开更多
The initial boundary value problem of a class of reaction-diffusion systems(coupled parabolic systems)with nonlinear coupled source terms is considered in order to classify the initial data for the global existence,fi...The initial boundary value problem of a class of reaction-diffusion systems(coupled parabolic systems)with nonlinear coupled source terms is considered in order to classify the initial data for the global existence,finite time blowup and long time decay of the solution.The whole study is conducted by considering three cases according to initial energy:the low initial energy case,critical initial energy case and high initial energy case.For the low initial energy case and critical initial energy case the sufficient initial conditions of global existence,long time decay and finite time blowup are given to show a sharp-like condition.In addition,for the high initial energy case the possibility of both global existence and finite time blowup is proved first,and then some sufficient initial conditions of finite time blowup and global existence are obtained,respectively.展开更多
This paper mainly studies the blowup phenomenon of solutions to the compressible Euler equations with general time-dependent damping for non-isentropic fluids in two and three space dimensions. When the initial data i...This paper mainly studies the blowup phenomenon of solutions to the compressible Euler equations with general time-dependent damping for non-isentropic fluids in two and three space dimensions. When the initial data is assumed to be radially symmetric and the initial density contains vacuum, we obtain that classical solution, especially the density, will blow up on finite time. The results also reveal that damping can really delay the singularity formation.展开更多
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In this article,we discuss the blowup phenomenon of solutions to the wdiffusion equation with Dirichlet boundary conditions on the graph.Through Banach fixed point theorem,comparison principle,construction of auxiliary function and other methods,we prove the local existence of solutions,and under appropriate conditions the blowup time and blowup rate estimation are given.Finally,numerical experiments are given to illustrate the blowup behavior of the solution.
文摘A nonlinear degenerate parabolic equation with nonlocal source was considered. It was shown that under certain assumptions the solution of the equation blows up in finite time and the set of blowup points is the whole region. The integral method is used to investigate the blowup properties of the solution.
基金Supported by NSF(No:10171083 and 10371021)of China Laboratory of Mathematics for Nonlinear Sciences of Fudan University
文摘In this paper we consider the existence and asymptotic estimates of global solutions and finite time blowup of local solutions of quasilinear parabolic equation with critical Sobolev exponent and with lower energy initial value; we also describe the asymptotic behavior of global solutions with high energy initial value.
基金upported by National Natural Science Foundation of China (Grant No. 11471087)the China Postdoctoral Science Foundation International Postdoctoral Exchange Fellowship Program+1 种基金the Heilongjiang Postdoctoral Foundation (Grant No. LBH-Z13056)the Fundamental Research Funds for the Central Universities
文摘The initial boundary value problem of a class of reaction-diffusion systems(coupled parabolic systems)with nonlinear coupled source terms is considered in order to classify the initial data for the global existence,finite time blowup and long time decay of the solution.The whole study is conducted by considering three cases according to initial energy:the low initial energy case,critical initial energy case and high initial energy case.For the low initial energy case and critical initial energy case the sufficient initial conditions of global existence,long time decay and finite time blowup are given to show a sharp-like condition.In addition,for the high initial energy case the possibility of both global existence and finite time blowup is proved first,and then some sufficient initial conditions of finite time blowup and global existence are obtained,respectively.
文摘This paper mainly studies the blowup phenomenon of solutions to the compressible Euler equations with general time-dependent damping for non-isentropic fluids in two and three space dimensions. When the initial data is assumed to be radially symmetric and the initial density contains vacuum, we obtain that classical solution, especially the density, will blow up on finite time. The results also reveal that damping can really delay the singularity formation.
