Decay of solutions for a system of higher-order wave equations

In the first chapter of this thesis, differential equations emerging in applied sciences, such as engineering and science, are briefly dealt with, and the basic information regarding decay of solutions is given. In the second chapter, the studies on high order nonlinear wave equations are summarized. In the third chapter, the basic concepts of differential equations, functional analysis and Sobolev spaces and some inequalities are given. After that, we used the lemma of energy reduction. In the first part of the fourth chapter, the existence of solutions of high order nonlinear viscoelastic wave equation is discussed. The second part of the thesis is the global existence and energy decay of the solutions of the higher order Kirchhoff type wave equation system has been proven.