Study On Two Kinds Of Coupled Wave Equations With Initial-boundary Values

In recent years, with the development of science and technology,the study of hyperbolic equations with damping and source terms gradually get more attention, especially the study of solutions for nonlinear wave equations, such as:global existence, stability, blow up, etc.In this paper we mainly discuss the initial boundary value problems for tow kinds of coupled wave equations with damping and source terms.First of all, by using energy method we discuss the initial boundary value problems for the following nonlinear coupled wave equations with damping and source terms and obtain the sufficient conditions of blow-up, global existence and asymptotic stability of solutions.Then, we discuss the problem of blow-up for coupled viscoelastic wave equations with strong damping as follows by using energy method we obtain blow up of solutions,this result is based on [25] and the equations are more generalized. The results are more general.The conclusions are based on former authors’ works and our results generalize the equations and the methods in [1,25,26].The equations are more difficulty and the results go further.