Well-posedeness of a semilinear viscoelastic equation with mixed Dirichlet and Neumann boundary conditions

The well-posedness of a class of nonlinear viscoelastic wave equations with mixed boundary conditions is investigated． The existence and uniqueness of regular solutions are established by classical Galerkin approximation method combined with the principle of compactness． A priori estimates are employed to demonstrate well-posedness of both generalized and weak solutions．