\(C^m\)-theory of damped wave equations with stabilisation

DOI10.1016/j.jmaa.2008.02.024zbMath1148.35043arXiv0711.2403OpenAlexW1975272030MaRDI QIDQ924240

Jens Wirth, Fumihiko Hirosawa

Publication date: 15 May 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.2403

zbMATH Keywords

wave equationsA priori estimatestime-dependent dissipationfast oscillations

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (11)

\(L^p-L^q\) estimates for wave equations with strong time-dependent oscillations ⋮ On \(t\)-dependent hyperbolic systems. II. ⋮ Energy estimates for the Cauchy problem of Klein-Gordon-type equations with non-effective and very fast oscillating time-dependent potential ⋮ Higher-order expansion of solutions for a damped wave equation ⋮ On the asymptotic behavior of the energy for evolution models with oscillating time-dependent damping ⋮ Large time behavior of solutions for a nonlinear damped wave equation ⋮ Generalized energy conservation for Klein-Gordon type equations ⋮ Large time behavior of global solutions of the semilinear damped beam equation with slowly decaying data ⋮ Dispersive estimates for hyperbolic systems with time-dependent coefficients ⋮ Theory of damped wave models with integrable and decaying in time speed of propagation ⋮ Generalised energy conservation law for wave equations with variable propagation speed

Cites Work

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• \(L^p\)-\(L^q\) estimate for wave equation with bounded time dependent coefficient
• Wave equations with time-dependent dissipation. I: Non-effective dissipation
• Wave equations with time-dependent dissipation. II: Effective dissipation
• Scattering and modified scattering for abstract wave equations with time-dependent dissipation
• Generalised energy conservation law for wave equations with variable propagation speed
• Energy decay of solutions to the wave equations with linear dissipation localized near infinity
• On the asymptotic behavior of the energy for the wave equations with time depending coefficients
• One application of Floquet's theory toLp-Lq estimates for hyperbolic equations with very fast oscillations
• Solution representations for a wave equation with weak dissipation
• Parameteric resonance and nonexistence of the global solution to nonlinear wave equations

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