On the decay property of solutions to the Cauchy problem of the semilinear beam equation with weak damping for large initial data

摘要

This paper is devoted to the study of the initial value problem for some semilinear damped beam equation which has a non-negative definite energy functional. We prove a uniform bound and decay estimates of a solution for the equation with large initial data using the method introduced by Kawashima-Nakao-Ono [3].