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

Takeda, Hiroshi; Yoshikawa, Shuji

doi:10.2969/aspm/06410507

VOL. 64 | 2015 On the decay property of solutions to the Cauchy problem of the semilinear beam equation with weak damping for large initial data

Chapter Author(s) Hiroshi Takeda, Shuji Yoshikawa

Editor(s) Shin-Ichiro Ei, Shuichi Kawashima, Masato Kimura, Tetsu Mizumachi

Adv. Stud. Pure Math., 2015: 507-514 (2015) DOI: 10.2969/aspm/06410507

Abstract

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].