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Wave equation with hyperbolic boundary condition: a frequency domain approach

Nicolas Vanspranghe 1 
1 GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics
GIPSA-PAD - GIPSA Pôle Automatique et Diagnostic
Abstract : In this paper, we investigate the stability of the linear wave equation where one part of the boundary, which is seen as a lower-dimensional Riemannian manifold, is governed by a coupled wave equation, while the other part is subject to a dissipative Robin velocity feedback. We prove that the closed-loop equations generate a semi-uniformly stable semigroup of linear contractions on a suitable energy space. Furthermore, under multiplier-related geometrical conditions, we establish a polynomial decay rate for strong solutions. This is achieved by estimating the growth of the resolvent operator on the imaginary axis.
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https://hal.archives-ouvertes.fr/hal-03781188
Contributor : Nicolas Vanspranghe Connect in order to contact the contributor
Submitted on : Wednesday, September 21, 2022 - 11:01:45 AM
Last modification on : Monday, December 5, 2022 - 11:30:55 AM

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  • HAL Id : hal-03781188, version 1
  • ARXIV : 2209.10872

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Nicolas Vanspranghe. Wave equation with hyperbolic boundary condition: a frequency domain approach. IFAC CPDE 2022 Workshop on Control of Systems Governed by Partial Differential Equations, Sep 2022, Kiel, Germany. ⟨hal-03781188⟩

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