Behaviour of solutions of evolution equations with degenerate damping terms

In the first chapter of this thesis, evolution equations emerging in applied sciences, such as engineering and science, are briefly dealt with. In addition, a brief information was given about the qualitative theory. In the second chapter, the historical development of the studies on equations with degenerate damping term, Kirchhoff equations and Timoshenko equations are considered. In the third chapter, basic definitions, lemma, theorems and inequalities that will be used throughout the thesis are given. Furthermore, modelling of Kirchhoff equation, modelling of Timoshenko equation and Galerkin approximation method are given. The fourth part is the original part of the thesis and consists of three sections. In the first section nonexistence of global solutions for the Timoshenko equation with degenerate damping term is studied. In the second section, general decay and blow-up of solutions for coupled viscoelastic equation of Kirchhoff-type with degenerate damping term are studied. In the last section local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping term are studied.