Details

Autor(en) / Beteiligte

• Colombini, Ferruccio
• Del Santo, Daniele
• Lannes, David

Titel

Second Microlocalization and Stabilization of Damped Wave Equations on Tori

Ist Teil von

• Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics, 2017, Vol.17, p.55-73

Ort / Verlag

Switzerland: Springer International Publishing AG

Erscheinungsjahr

2017

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this talk we present some recent results obtained in collaboration with P. Gérard (Stabilization of wave equations with rough dampings, 2016, in preparation) on the damped wave equation on two dimensional tori. With continuous dampings, the classical geometric control condition is necessary and sufficient for uniform stabilization. We give a very simple necessary and sufficient geometric condition on two dimensional tori for uniform stabilization in the special case where a(x)=∑j=1Naj1x∈Rj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a(x) =\sum _{ j=1}^{N}a_{j}1_{x\in R_{j}}$$\end{document} (Rj are rectangles, or more general polygons). The proof relies on second microlocalization.