Extinction Of Solution For The Nonlinear Parabolic Equations

Abstract The phenomena of extinction in finite time is an important property for solution of nonlinear equation,which have evident background,and have been extensively used to heat transports,chemical reactions,the diffusion oforganism,elasticy and star's develop,etc.In recent years, the phenomena of extinction for solutions of nonlinear equations have been extensively studied by many authors, which use energy methods, comparison piniple and eigenfunction arguments,etc,and a lot of resultshave been proved.In this paper,with energy estimates and comparison prinaple,the sufficient conditions for extinction of solutions to a nonlinear parabolic equations or parabolic equation with gradient term will be considered,and the results will be extenced to highter-problems and p-laplacion equations.