Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 70, Number 4 (2018), 1375-1418.
Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation
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.
J. Math. Soc. Japan, Volume 70, Number 4 (2018), 1375-1418.
Received: 31 March 2017
First available in Project Euclid: 6 September 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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