Global nonexisting (blow up) of solutions in nonlinear parabolic or hyperbolic differential equations

vıı SUMMARY In this thesis, the global nonexistence (blow up) of solutions to the initial boundary problems for some parabolic and hyperbolic type differential equations of which their boundary values equal to zero is investigated. In the first chapter, so far the studies done with the historical developments are shortly given about the blow up. Some notations and fundamental definitions which are necessary for the remaining chapters of the thesis are presented in the second chapter. In the third chapter, the subject of singularity formation in differential equations usually known as blow up is presented and the classical questions addressed by the blow up theory is discussed. In the fourth chapter, methods of establishing global nonexistence (blow up) and growth of solutions in finite time are presented. In the fifth chapter, we proved the blow up of solutions to the initial boundary value problem for a class of nonlinear wave equations with a damping term by using explicit inequality methods. In the sixth chapter, we proved the blow up of solutions to the initial boundary value problem for Boussinesq equation with damping term by using explicit inequality methods. In the seventh chapter, we proved the blow up of solutions to the initial boundary value problem for the improved Boussinesq equation with damping term by using explicit inequality methods. In the eighth chapter, we proved the blow up of solutions to the initial boundary value problem for a class of nonlinear wave equation with nonlinear damping term by using explicit inequality methods.