Sharp decay rates for wave equations with a fractional damping via new method in the Fourier space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:408

Article

Charao, Ruy Coimbra¹  da Luz, Cleverson Roberto¹  Ikehata, Ryo² 

[1] Univ Fed Santa Catarina, Dept Math, BR-88040900 Florianopolis, SC, Brazil

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

关键词: Wave equation;    Fractional damping;    Total energy decay;    Multiplier method;    Fourier analysis;    Low frequency;    High frequency;    The Haraux-Komornik inequality;   

DOI  :  10.1016/j.jmaa.2013.06.016

来源: Elsevier

【 摘 要 】

We study the Cauchy problem for damped wave equations with a fractional damping (-Delta)(theta)u(t) in R-n. We derive more sharp decay estimates of the total energy based on the energy method in the Fourier space combined with the Haraux-Komornik inequality. Especially, in the case when 0 <= theta <= 1/2 the rate of decay of the total energy becomes almost optimal. The method in this paper can be applied to other equations and in particular it seems to be quite effective in the case of frictional dissipation, i.e., when theta = 0. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free