Journal of the Mathematical Society of Japan

Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation

Romain JOLY and Julien ROYER

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Abstract

We prove local and global energy decay for the asymptotically periodic damped wave equation on the Euclidean space. Since the behavior of high frequencies is already mostly understood, this paper is mainly about the contribution of low frequencies. We show in particular that the damped wave behaves like a solution of a heat equation which depends on the H-limit of the metric and the mean value of the absorption index.

Article information

Source
J. Math. Soc. Japan, Volume 70, Number 4 (2018), 1375-1418.

Dates
Received: 31 March 2017
First available in Project Euclid: 6 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1536220816

Digital Object Identifier
doi:10.2969/jmsj/77667766

Mathematical Reviews number (MathSciNet)
MR3868211

Zentralblatt MATH identifier
07009706

Subjects
Primary: 35L05: Wave equation
Secondary: 35B40: Asymptotic behavior of solutions 47B44: Accretive operators, dissipative operators, etc. 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50] 47A10: Spectrum, resolvent

Keywords
damped wave equation energy decay diffusive phenomenon periodic media

Citation

JOLY, Romain; ROYER, Julien. Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation. J. Math. Soc. Japan 70 (2018), no. 4, 1375--1418. doi:10.2969/jmsj/77667766. https://projecteuclid.org/euclid.jmsj/1536220816


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