THE WAVE EQUATION ON A THIN DOMAIN: ENERGY DENSITY AND OBSERVABILITY
Gilles A. Francfort, Patrick Gérard · Journal of Hyperbolic Differential Equations · 2004
We compute the limit energy density of solutions of the linear wave equation in a thin three-dimensional domain, if the wavelength of the Cauchy data is bounded from below by the thickness of the domain. As an application, we obtain a geometric criterion for the uniform observability of solutions of a damped wave equation on such a domain.