Liouville's Theorem For Some Parabolic Partial Differential Equations And Its Stable Solution

In this paper,on the basis of Enzo mitidieri and Stanislav I.pohozaev's research on the solutions of parabolic partial differential equations,we further study the stability of the solutions of the parabolic partial differential equations.This paper is divided into the following two parts:In the first part,we study the nontrivial stable weak solutions of a class of simple parabolic partial differential equations.First,we prove the existence conditions of the nontrivial weak solutions of the equations by Young inequality,test function and variable substitution,and then further strengthen the conditions of the nontrivial weak solutions of parabolic partial differential equations according to the conditions of the stable solutions of partial differential equations.The second part is the problem of nontrivial stable weak solutions for a class of p-Laplace parabolic partial differential equations.We prove the existence conditions of nontrivial weak solutions for p-Laplace parabolic partial differential equations by using a priori estimation method,and then further strengthen the conditions of nontrivial weak solutions for p-Laplace parabolic partial differential equations according to the conditions of stable solutions for partial differential equations.