On the Neumann-Dirichlet problem for a system of nonlinear viscoelastic equations of Kirchhoff type with Balakrishnan- Taylor term

In this paper, the Neumann-Dirichlet boundary problem for a system of nonlinear viscoelastic equations Kirchhoff type with Balakrishnan-Taylor term is considered. At first, local existence established by linear approximation together Faedo- Galerkin method. Then, establishing several reasonable conditions and suitable energy inequalities, solution admits general decay in time.