EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR A STRONGLY DAMPED WAVE EQUATION WITH POLYNOMIAL NONLINEARITIES

Abstract

This paper studies the first initial boundary value problem for the strongly damped wave equations on a bounded domain   3 . Under the polynomial growth rate of the nonlinearity f and an external force g independent on time t, we prove the existence and uniqueness of a weak solution. Finally, we show the existence of a weak global attractor for the continuous semigroup generated by the weak solution.