Wave equation with hyperbolic boundary condition: a frequency domain approach
Analysis of PDEs
2022-09-23 v1 Optimization and Control
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.
Keywords
Cite
@article{arxiv.2209.10872,
title = {Wave equation with hyperbolic boundary condition: a frequency domain approach},
author = {Nicolas Vanspranghe},
journal= {arXiv preprint arXiv:2209.10872},
year = {2022}
}