Observability of a Ring Shaped Membrane via Fourier Series

Abstract : We study the inverse Ingham type inequality for a wave equation in a ring. This leads to a conjecture on the zeros of Bessel cross product functions. We motivate the validity of the conjecture through numerical results. We do a complete analysis in the particular case of radial initial data, where an improved time of observability is available.
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Vilmos Komornik, Paola Loreti, Michel Mehrenberger. Observability of a Ring Shaped Membrane via Fourier Series. 27th IFIP Conference on System Modeling and Optimization (CSMO), Jun 2015, Sophia Antipolis, France. pp.322-330, ⟨10.1007/978-3-319-55795-3_30⟩. ⟨hal-01626896⟩

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