Competition Between Damping Terms And Sources Terms Causes Influence On The Local Existence And Global Existence To The Solutions

This thesis deals with two problems for a class of nonlinear wave equations with fractional order derivative damping. Firstly, this thesis discusses the local existence to the initial-boudary problem of some nonlinear wave equations with fractional order derivative damping, then we discuss the global existence and blow-up results to the same problem.In chapter one, we review the importance and some backgrounds of recent study for this kind of nonlinear wave equations with fractional order derivative damping.In chapter two, several different definitions are expounded about fractional order derivative. And the reason why we use the Caputo definition about fractional order derivative during the course of the study on nonlinear wave equations with damping terms and sources terms was given.In chapter three, we discuss a class of nonlinear wave equations with fractional order derivative damping and polynomial damping terms and sources term. The local existence to the solutions was proved.In chapter four, we discuss a class of nonlinear wave equations with fractional order derivative damping and polynomial damping terms and sources term. The global existence to the solutions was proved for 1m >1.Finaly, in the condition of competition between different damping terms and sources terms diffierent influence on local existence and global existence will be discussed to nonlinear wave equations with fractional order derivative in the future.