Asymptotic Boundary Observability for the Wave Equation on One Side of a Planar Triangle

Abstract

We consider the wave equation $({\partial }_t^2-\Delta )u=0$ on a planar triangular domain $\Omega \subset {\mathbb{R}}^2$ with Dirichlet boundary conditions. We use a commutator and integration by parts argument similar to that in \cite{Chr2DTriangles} by the first author to obtain an observability asymptotic for any one side of the triangle. Our result is particular to triangular domains and does not hold for polygons in general.