Nonexistence of Solution for Higher Order Evolution Equations and Inequalities

Abstract

Many authors have established results for existence and nonexistence of nonlinear evolution P.D.Es in the form $\f{\partial^k u}{\partial t^k}-\delta_1\triangle u+\delta_2\Delta^2 u=f(x,\nabla u,u)$ where $\delta_1,\delta_2\in \{0,1\}$. In this paper we will prove the nonexistence results for the general form that contains this forms for $f(x,\nabla u,u)=|x|^{-\gamma}|u|^q$ or $|u|^q$ or $|\nabla u^q|^p$.