Blow up of solutions for Timoshenko equation with damping term

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 blow up of solutions is given. In the second chapter, the studies concerning Timoshenko equation with damping term are summarized. In the third chapter, elementary notions and some inequalities about Sobolev spaces, functional analysis and differential equations are presented. Subsequently, the lemmas that we have used to prove the blow up of the solutions is presented. In the fourth chapter, primarily, the definitions pertaining to the beam theory are given, and then, the modeling of Timoshenko equation is presented. The final part involves the original part of the thesis, in which the blow up of the solutions has been proven for negative, zero and positive initial energy.