General Decay Of Solutions Of Two Classes Of Viscoelastic Wave Equations

In modern mathematics,there is an important branch of nonlinear partial differential equations.In the fields of theory and practical applications of physics,chemistry,biology and economics,viscoelastic wave equations and its coupled systems are very common equations,which have been attracting many mathematics workers.Much biological and engineering material and as well as the deformation state of metal materials in high speed,has viscoelastic properties.So,viscoelastic equations have theoretical significance and practical significance.In this paper,we study the properties of solutions of two classes of viscoelastic wave equations.First of all,we discuss the following viscoelastic wave equation with Balakrishnan-Taylor damping terms,We use perturbed energy functional technique to give the results of the local existence,the global existence and the asymptotic stability of the solution.Secondly,we discuss the following coupled system of nonlinear viscoelastic wave equa-tions,We obtain a general decay result of solutions,which depends on the behavior of the relaxation function g and a by using multiplier techniques and perturbed energy functional technique.