Decay and blow up of solutions of nonlinear evolution equations

In the first chapter of this thesis the historical developments of the decay and blow up of solutions are investigated. In the second chapter, basic definitions, theorems and inequalities that will be used throughout the thesis are given. In the third chapter, some basic lemmas about the decay and blow up of solutions, used in the thesis, are given with their proofs. In the fourth chapter, local and global existence, energy decay and blow up of solutions are studied for a system of wave equation with nonlinear damping and source terms. In the fifth chapter, the energy decay and blow up of solutions for a higher order system with weak damping term are studied. In the sixth chapter, global existence, energy decay and blow up of solutions are studied for a higher order systems with strong damping, nonlinear damping and source terms.