Methods and Applications of Analysis

Volume 12 (2005)

Number 1

Nonexistence of Solution for Higher Order Evolution Equations and Inequalities

Pages: 1 – 18

DOI: http://dx.doi.org/10.4310/MAA.2005.v12.n1.a1

Authors

Hirbod Assa

Mahmoud Hesaaraki

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 $|\nabla u^q|^p$.

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