This paper deals with a class of porous medium equation ut=△u^m＋f（u）with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on...This paper deals with a class of porous medium equation ut=△u^m＋f（u）with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on the function f（u）.展开更多
This paper is concerned with a system of nonlinear viscoelastic wave equations with degenerate nonlocal damping and memory terms.We will prove that the energy associated to the system is unbounded.In fact,it will be p...This paper is concerned with a system of nonlinear viscoelastic wave equations with degenerate nonlocal damping and memory terms.We will prove that the energy associated to the system is unbounded.In fact,it will be proved that the energy will grow up as an exponential function as time goes to infinity,provided that the initial data are positive initial energy.展开更多
We investigate the p-Laplace heat equation ut-△_(p)u=ζ(t)f(u)in a bounded smooth domain.Using differential-inequality arguments,we prove blow-up results under suitable conditions onζ,f,and the initial datum u_(0).W...We investigate the p-Laplace heat equation ut-△_(p)u=ζ(t)f(u)in a bounded smooth domain.Using differential-inequality arguments,we prove blow-up results under suitable conditions onζ,f,and the initial datum u_(0).We also give an upper bound for the blow-up time in each case.展开更多
基金The project is supported by NSFC(11271154)Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Educationby the 985 Program of Jilin University
文摘This paper deals with a class of porous medium equation ut=△u^m＋f（u）with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on the function f（u）.
基金Supported by the National Natural Science Foundation of China(Grant No.11801145)。
文摘This paper is concerned with a system of nonlinear viscoelastic wave equations with degenerate nonlocal damping and memory terms.We will prove that the energy associated to the system is unbounded.In fact,it will be proved that the energy will grow up as an exponential function as time goes to infinity,provided that the initial data are positive initial energy.
文摘We investigate the p-Laplace heat equation ut-△_(p)u=ζ(t)f(u)in a bounded smooth domain.Using differential-inequality arguments,we prove blow-up results under suitable conditions onζ,f,and the initial datum u_(0).We also give an upper bound for the blow-up time in each case.
