Mathematics > Analysis of PDEs
[Submitted on 29 Nov 2018]
Title:Asymptotic Boundary Observability for the Wave Equation on One Side of a Planar Triangle
View PDFAbstract: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.
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