Mathematical behavior of solution of nonlinear timoshenko equation

In the first chapter of this thesis, the abbreviations and notations that will be used throughout this thesis are provided. In the second chapter, the historical developments of the blow up of solutions are investigated. In the third chapter, the basic definitions, theorems, and inequalities that will be used in this thesis are provided. The fourth chapter is composed of three sub-sections. In the first sub-section, the local existence of solutions of Timoshenko equations that contain nonlinear damping and source terms are examined. In the second sub-section, the blow up of solutions for the equation with the initial negative energy is investigated. In the final sub-section, which also forms the main part of this thesis, the blow up of solutions for positive initial energy is studied. Keywords: Blow up, Local existence, Nonlinear Timoshenko equation.