Wave equations with strong damping in Hilbert spaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:254

Article

Ikehata, Ryo¹  Todorova, Grozdena²  Yordanov, Borislav² 

[1] Hiroshima Univ, Grad Sch Educ, Dept Math, Higashihiroshima 7398524, Japan

[2] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

关键词: Strongly damped wave equation;    Multiplier method;    Fourier analysis;    Spectral analysis;    Total energy decay;    Low frequency;    High frequency;   

DOI  :  10.1016/j.jde.2013.01.023

来源: Elsevier

【 摘 要 】

We study the Cauchy problem for abstract dissipative equations in Hilbert spaces generalizing wave equations with strong damping terms in R-N or exterior domains. Our main result is a generalized diffusion phenomenon: the long time asymptotics of strongly damped wave equations is a combination of solutions of diffusion and wave equations. In particular, we obtain sharp decay estimates. The proofs rely on the energy method in the Fourier space and its generalization based on the spectral theorem for self-adjoint operators. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free