Dynamic Properties For Two Classes Of Nonlinear Reaction-diffusion Equations

It plays an important role in the control problem of many nonlinear models for nonlinear reaction-diffusion equations,which are used to describe various processes in physics,chemistry,biology,and so on.In this paper,the existence,blow-up and extinction of solutions for two classes of logarithmic nonlinear reaction-diffusion equations are studied by virtue of potential well method,Galerkin approximation,comparison principle and partial differential inequality techniques.Firstly,we consider the initial boundary value problem for a class of logarithmic nonlinear pseudo-parabolic equations ut-a?ut-?u+bu=|u|p-2ulog|u|.The global existence of weak solutions are obtained by the methed of Galerkin approximation in case of 1