The Multidimensional Wave Equation with Generalized Acoustic Boundary Conditions I: Strong Stability

2015/01/01 by Z. Abbas, Zainab Abbas, Serge Nicaise +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations

paper · doi:10.1137/140971336

openalex publication_date 2015/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the wave equation on a domain of ℝ^d, d≥ 2, with dynamical boundary control applied on a part of the boundary and a Dirichlet boundary condition on the remaining part. We prove the asymptotic stability and nonuniform stability of the associated semigroup.

Citations

• On the spectrum of 𝐶₀-semigroups
• Optimal polynomial decay of functions and operator semigroups
• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
• Stabilisation de l’équation des ondes par le bord

Cited by

• Controllability and mixing for acoustic wave motions