SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research

Global existence and asymptotic behavior of solutions to a class of fourth-order wave equations

Zhitao Zhuang and Yuanzhang Zhang*

Author Affiliations

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 2013, 2013:168  doi:10.1186/1687-2770-2013-168

Published: 16 July 2013

Abstract

This paper is concerned with the Cauchy problem for a class of fourth-order wave equations in an n-dimensional space. Based on the decay estimate of solutions to the corresponding linear equation, a solution space is defined. We prove the global existence and optimal decay estimate of the solution in the corresponding Sobolev spaces by the contraction mapping principle provided that the initial value is suitably small.

MSC: 35L30, 35L75.

Keywords:
fourth-order wave equation; global existence; decay estimate