Study On The Properties Of Solutions Of Two Classes Of Coupled Wave Equations

Partial differential equations,which are derived from a variety of practical problems,arise in many fields.Wave equations are very important partial differential equations.Manyimportant results have been proved in the study of linear wave equations,such as the ex-istence,stability,regularity and so on,have a systematic theoretical results.However,itis complex to solve nonlinear wave equations.Its important to study the properties of thesolutions to the nonlinear wave equations.In this paper,we study the properties of solutionsof two classes of coupled wave equations.First of all,we discuss the properties of the solutions of nonlinear coupled wave equationswith initial-boundary value conditions,We give the results of the local existence,the global existence and the blow-up of the solu-tions.Secondly,we discuss the coupled viscoelastic wave equations with initial-boundary value conditions,By using the perturbed energy method,we study the general decay of the solutions.