Generalized energy conservation for Klein-Gordon type equations

zbMath1250.35133MaRDI QIDQ436045

Fumihiko Hirosawa, Christiane Böhme

Publication date: 28 July 2012

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ojm/1340197927

zbMATH Keywords

Fourier transformenergy estimatesKlein-Gordon equationGevrey classgeneralized energy conservation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) A priori estimates in context of PDEs (35B45) Perturbations in context of PDEs (35B20) Initial value problems for second-order hyperbolic equations (35L15)

Related Items

Energy estimates for the Cauchy problem of Klein-Gordon-type equations with non-effective and very fast oscillating time-dependent potential ⋮ Energy bounds for Klein-Gordon equations with time-dependent potential ⋮ A scale-invariant Klein-Gordon model with time-dependent potential

Cites Work

• Energy bounds for Klein-Gordon equations with time-dependent potential
• \(L^p\)-\(L^q\) estimate for wave equation with bounded time dependent coefficient
• Wave equations with time-dependent dissipation. II: Effective dissipation
• \(C^m\)-theory of damped wave equations with stabilisation
• Energy estimates for wave equations with time dependent propagation speeds in the Gevrey class
• 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
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