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Asymptotic Boundary Observability For The Wave Equation On Simplices

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arxiv 2004.01748 v1 pith:OB67EZY7 submitted 2020-04-03 math.AP

Hans Christianson , Ziqing Lu This is my paper · ORCID
classification math.AP
keywords asymptoticboundaryequationobservabilityresultsimplexwaveaspects
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In this paper, we consider the wave equation on an n-dimensional simplex with Dirichlet boundary conditions. Our main result is an asymptotic observability identity from any one face of the simplex. The novel aspects of the result are that it is a large-time asymptotic rather than an estimate, and it requires no dynamical assumptions on the billiard flow. The proof uses mainly integrations by parts.

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