On the energy estimates of the wave equation with time dependent propagation speed asymptotically monotone functions

DOI10.1016/J.JMAA.2015.06.051zbMath1330.35050OpenAlexW2202652987MaRDI QIDQ493792

Fumihiko Hirosawa, Laila Fitriana, Marcelo Rempel Ebert

Publication date: 4 September 2015

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.06.051

zbMATH Keywords

lower and upper bounds for the energy

Mathematics Subject Classification ID

Wave equation (35L05) A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (6)

Energy estimates for the Cauchy problem of Klein-Gordon-type equations with non-effective and very fast oscillating time-dependent potential ⋮ Optimal derivative loss for abstract wave equations ⋮ On the energy estimates of semi-discrete wave equations with time dependent propagation speed ⋮ Critical counterexamples for linear wave equations with time-dependent propagation speed ⋮ Asymptotically free property of the solutions of an abstract linear hyperbolic equation with time-dependent coefficients ⋮ Theory of damped wave models with integrable and decaying in time speed of propagation

Cites Work

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• On second order weakly hyperbolic equations and the ultradifferentiable classes
• On the asymptotic behavior of the energy for the wave equations with time depending coefficients
• On the Global Solvability for Semilinear Wave Equations with Smooth Time Dependent Propagation Speeds
• On second order weakly hyperbolic equations with oscillating coefficients and regularity loss of the solutions
• On the Gevrey well-posedness for second order strictly hyperbolic Cauchy problems under the influence of the regularity of the coefficients

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