Global existence and asymptotic behavior of solutions to a class of fourth-order wave equations
School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou, 450011, China
Boundary Value Problems 2013, 2013:168 doi:10.1186/1687-2770-2013-168Published: 16 July 2013
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.