EXISTENCE, BLOW-UP AND EXPONENTIAL DECAY FOR A NONLINEAR KIRCHHOFF-CARRIER-LOVE EQUATION WITH DIRICHLET CONDITIONS

Abstract

In this paper, we consider the initial boundary value problem for a nonlinear Kirchhoff-Carrier-Love equation. At first, by combining the linearization method, the Faedo-Galerkin method and the weak compactness method, we prove the local existence and uniqueness of a weak solution. Next, by constructing Lyapunov functional, we establish a blow-up result for solutions with a negative initial energy and give a sufficient condition to obtain the exponential decay of weak solutions.