Optimal decay rate for the wave equation on a square with constant damping on a strip

DOI10.1007/s00033-017-0781-0zbMath1404.35055arXiv1607.03633OpenAlexW2466519939MaRDI QIDQ2359011

Reinhard Stahn

Publication date: 27 June 2017

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.03633

zbMATH Keywords

Dirichlet boundary conditionsresolvent estimates\(C_0\)-semigroupsdamped wave equationpolynomial decaypiecewise constant damping

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) One-parameter semigroups and linear evolution equations (47D06) Wave equation (35L05)

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Cites Work

• Optimal energy decay in a one-dimensional coupled wave-heat system
• Optimal polynomial decay of functions and operator semigroups
• Non-uniform stability for bounded semi-groups on Banach spaces
• Energy decay for damped wave equations on partially rectangular domains
• Energy decay for a locally undamped wave equation
• Characterization of polynomial decay rate for the solution of linear evolution equation
• Sharp polynomial decay rates for the damped wave equation on the torus
• Vector-valued Laplace Transforms and Cauchy Problems
• Solutions of the wave equation with localized energy

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