Global Solution and Asymptotic Behaviour for a Wave Equation type p-Laplacian with Memory

In this work we study the global solution, uniqueness and asymptotic behaviour of the nonlinear equation u t t – Δ p u = Δ u – g ∗ Δ u where Δ p u is the nonlinear p -Laplacian operator, p ≥ 2 and g ∗ Δ u is a memory damping. The global solution is constructed by means of the Faedo-Galerkin approximations taking into account that the initial data is in appropriated set of stability created from the Nehari manifold and the asymptotic behavior is obtained by using a result of P. Martinez based on new inequality that generalizes the results of Haraux and Nakao.