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arXiv · 2209.10872

Wave equation with hyperbolic boundary condition: a frequency domain approach

Nicolas Vanspranghe
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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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Nicolas Vanspranghe. 2022-09-22. Wave equation with hyperbolic boundary condition: a frequency domain approach. https://arxiv.org/abs/2209.10872

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