SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research

Asymptotic profile of solutions to the semilinear beam equation

Yunpeng Zhang1* and Yanling Li2

Author Affiliations

1 College of Electric Power, North China University of Water Resources and Electric Power, Zhengzhou, 450011, China

2 School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou, 450011, China

For all author emails, please log on.

Boundary Value Problems 2014, 2014:84  doi:10.1186/1687-2770-2014-84

Published: 17 April 2014

Abstract

In this paper, we investigate the initial value problem for the semilinear beam equation. Under a small condition on the initial value, we prove the global existence and optimal decay estimate of solutions. Moreover, we show that as time tends to infinity, the solution is asymptotic to a diffusion wave, which is given explicitly in terms of the solution of parabolic equation.

MSC: 35L30, 35L75.

Keywords:
beam equation; decay estimate; asymptotic profile; diffusion wave