Global Existence of Mild Solutions for the Elastic System with Structural Damping

Abstract

In this paper, we study the global existence of mild solutions for the semilinear initial-value problems of second order evolution equations, which can model an elastic system with structural damping. This discussion is based on the operator semigroups theory and the Leray-Schauder fixed point theorem. In addition, an example is presented to illustrate our theoretical result.