## Journal of the Mathematical Society of Japan

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

#### 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
First available in Project Euclid: 6 September 2018

https://projecteuclid.org/euclid.jmsj/1536220816

Digital Object Identifier
doi:10.2969/jmsj/77667766

Mathematical Reviews number (MathSciNet)
MR3868211

Zentralblatt MATH identifier
07009706

#### 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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