Global Existence and Asymptotic Behavior for some Classes of Partial Differential Equations with Delay

Abstract

The main goal of this thesis is to study the global existence, general decay, and blow-up results of solutions for some nonlinear evolutions equations with different types of boundary conditions and delay terms. This work consists of three chapters: In chapter 1, we give some notations, present our assumptions and main results and some main theorems in functional analysis. Chapter 2 is devoted to study an initial boundary value problem for a Kirchhoff-type equation with nonlinear boundary delay and source terms. In chapter 3, we study a viscoelastic Kirchhoff plate equation with dynamic boundary conditions, delay and source terms acting on the boundary. The global existence of solutions has been obtained by potential well theory, the general decay result of energy has been established by introducing suitable energy and Lyapunov functionals, and the blow up result of solutions based on the method of Georgiev and Todorova.