Mathematical behavior of solutions of nonlinear hyperbolic partial differential equations

In this thesis, mathematical behavior of solutions of some partial differential equations which are hyperbolic type is investigated.In the first chapter, the historical development of studies related to partial differential equations up to now is shortly discussed.In the second chapter, some fundamental definitions and notations which are necessary for the following chapters are given.In the third chapter, weak solutions of the second order hyperbolic equations are defined.In the fourth chapter, asymptotic behavior of a forth order wave equations with dissipative and dispersive terms is investigated.In the last chapter, local and global existence, continuous dependence on initial data and asymptotic behavior of a sixth order Cauchy problem with damping is proved.