Nonexistence Of Weak Solutions For A Class Of Nonlinear Evolution Inequality Equations

In recent years,nonlinear problems have appeared in many fields,and then nonlinear problems have attracted extensive attention.Many of them can be attributed to the study of nonlinear evolution equations,which can describe the actual phenomena of these research problems,Therefore,it is important to analyze the parabolic inequality equations with p-Laplace type Baouendi-Grushin operator,especially in the fields of physics,biology,non-Newtonian fluid in porous media,gas flow.At present,there are many research results on the solutions of parabolic inequality equations with p-Laplace type Baouendi-Grushin operator.This paper mainly studies the nonexistence of weak solutions for a class of nonlinear evolution inequality equations,which includes two parts:In the first part,the nonexistence of weak solutions for a class of parabolic inequality equations with p-Laplace type Baouendi-Grushin operator is analyzed by using a priori estimation and improved test function method,the nonexistence of weak solutions of this kind of equation under relevant conditions is proved by appropriate variable transformation.It is further extended to analyze the nonexistence of weak solutions of more general equations and prove the nonexistence of weak solutions.In the second part,a priori estimate is obtained according to the ideas and methods of the first part,the nonexistence of weak solutions of a weighted parabolic inequality equation with p-Laplace type Baouendi-Grushin operator is analyzed by the test function method,and the nonexistence of weak solutions of this kind of equation under relevant conditions is proved.