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

Romain Joly (1) , Julien Royer (2)

1 IF - Institut Fourier
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: energy decay; Damped wave equation; diffusive phenomenon; periodic media.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Romain Joly, Julien Royer. Energy decay and diffusion phenomenon for the asymptotically periodic damped wave equation. Journal of the Mathematical Society of Japan, 2018, 70 (4). ⟨hal-01490420⟩