Asymptotic behaviour of solution for multidimensional viscoelasticity equation with nonlinear source term

In this paper we study the initial-boundary value problem of multidimensional viscoelasticity equation with nonlinear source term. By using potential well method we first prove the global existence. Then we prove that when time $t\to +\infty $ the solution decays to zero exponently under some assumptions on nonlinear functions and the initial data.