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One dimensional wave equation with in-domain localized damping and Wentzell boundary conditions (2503.22439v1)

Published 28 Mar 2025 in math.AP and math.OC

Abstract: This paper is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary conditions. In a quite general boundary setting, we establish the exponential decay of solutions towards the corresponding steady states. The results are obtained either by the multiplier method or spectral analysis in an $L2$-functional framework, and then with input-to-state technics in an $Lp$-functional framework for $p \in (2,\infty)$.

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