Remarks on the asymptotic behavior of the solution to damped wave equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Nishiyama, Hisashi¹ 

[1] Wakayama Univ, Dept Educ, 930 Sakaedani, Wakayama, Wakayama 6408510, Japan

关键词: Damped wave equation;    Heat equation;    Diffusion phenomena;    Geometric control condition;    Variable damping;    Energy decay;   

DOI  :  10.1016/j.jde.2016.06.014

来源: Elsevier

【 摘 要 】

We study the diffusion phenomena for damped wave equations. We prove that the solution of an abstract damped wave equation becomes closer to the solution of a heat type equation as time tends to infinity under some assumption to the resolvent. As an application of our approach, we also study the asymptotic behavior of the damped wave equation in Euclidean space under the geometric control condition. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free