Blow up of solutions for a singular integral equations

In the first chapter of this thesis, briefly information are given about differential equation and information are given about the blow up of solutions at the basic level. In the second chapter, previous studies on the blow up of solutions are given. In the third chapter, basic definitions, lemmas, theorems, inequalities and equations that may be required throughout the thesis are given. The fourth chapter consists of three parts. In the first part, the blow up of the solutions of the nonlocal singular viscoelastic equation is studied by the Georgiev and Todorova method. In the second part, the blow up of the solutions of the nonlocal singular viscoelastic equation system is studied by the Li-Tsai method. The third part is the original part of the thesis. In this part, the blow up of the solutions of the nonlocal singular viscoelastic equation system with nonlinear damping term is studied by the Georgiev and Todorova method.