LOCAL EXISTENCE AND EXPONENTIAL DECAY OF SOLUTIONS FOR A NONLINEAR PSEUDOPARABOLIC EQUATION WITH VISCOELASTIC TERM

Abstract

In this paper, we investigate an initial boundary value problem for a nonlinear pseudoparabolic equation. At first, by applying the Faedo-Galerkin, we prove local existence and uniqueness results. Next, by constructing Lyapunov functional, we establish a sufficient condition to obtain the global existence and exponential decay of weak solutions.