Mathematical behavior of solutions of nonlinear partial differential equations

In the first chapter of this thesis historical development of the equations which will be investigated in the next chapters, and relevant literature are given.In the second chapter, basic definitions, theorems and lemmas that will be used throughout the thesis are given.In the third chapter, the first method used in this thesis, the potential well method, is explained and related literature is given. Moreover, global existence and blow up of solutions of a problem is given by aid of this method.In the fourth chapter, the second method of the thesis, namely stationary phase method is mentioned.In the fifth chapter, local and global existence and blow up is investigated for a purely spatial sixth order good Boussinesq-type equation by potential well method. Moreover, blow up of solutions is given for a purely spatial sixth order bad Boussinesq-type equation.In the sixth chapter, a sixth order Boussinesq-type equation with supercritical initial energy is investigated by aid of potential well method.The seventh chapter contains local and global existence and decay of solutions for a bad Boussinesq type equation. The behavior of solutions is studied by stationary phase method.