One-dimensional wave equation with set-valued boundary damping: well-posedness, asymptotic stability, and decay rates

@article{Chitour2020OnedimensionalWE,
  title={One-dimensional wave equation with set-valued boundary damping: well-posedness, asymptotic stability, and decay rates},
  author={Y. Chitour and S. Marx and Guilherme Mazanti},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
This paper is concerned with the analysis of a one dimensional wave equation $z_{tt}-z_{xx}=0$ on $[0,1]$ with a Dirichlet condition at $x=0$ and a damping acting at $x=1$ which takes the form $(z_t(t,1),-z_x(t,1))\in\Sigma$ for every $t\geq 0$, where $\Sigma$ is a given subset of $\mathbb R^2$. The study is performed within an $L^p$ functional framework, $p\in [1, +\infty]$. We aim at determining conditions on $\Sigma$ ensuring existence and uniqueness of solutions of that wave equation as… Expand

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