On energy estimates for second order hyperbolic equations with Levi conditions for higher order regularity

DOI10.1007/S11565-011-0121-9zbMath1253.35025OpenAlexW2039818658MaRDI QIDQ1762234

Fumihiko Hirosawa, Tang Bao Ngoc Bui

Publication date: 15 November 2012

Published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11565-011-0121-9

zbMATH Keywords

wave equationdissipationenergy estimatetime dependent coefficientsLevi conditionsgeneralized energy conservation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (1)

Time-dependent propagation speed vs strong damping for degenerate linear hyperbolic equations

Cites Work

• \(L^p\)-\(L^q\) estimate for wave equation with bounded time dependent coefficient
• \(L^p\)-\(L^q\) estimates for regularly linear hyperbolic systems
• On the asymptotic behavior of the energy for the wave equations with time depending coefficients
• Levi condition for hyperbolic equations with oscillating coefficients
• On the Gevrey well-posedness for second order strictly hyperbolic Cauchy problems under the influence of the regularity of the coefficients
• NECESSARY CONDITIONS FOR THE CAUCHY PROBLEM FOR NON-STRICTLY HYPERBOLIC EQUATIONS TO BE WELL-POSED
• Loss of regularity for the solutions to hyperbolic equations with non-regular coefficients?an application to Kirchhoff equation
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