Existence and Non-existence of Global Solutions to Initial Boundary Value Problems for Nonlinear Evolution Equations with the Strong Dissipation

Abstract

The main purpose in this paper is to investigate existence and non-existence of global solutions of the initial Dirichlet-boundary value problem for evolution equations with the strong dissipation. Many authors studied classes consisting of such type of equations for which initial boundary value problems possess global solutions. For this purpose we consider a related problem and seek global solutions and blow-up solutions of it depending on whether it belongs to such classes or not. Key words: evolution equation, strong dissipation, blow-up, global existence 2000 MSC: 35L70, 35L15, 35L20, 58K55 1