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

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].