A remark on parametric resonance for wave equations with a time periodic coefficient

DOI10.3792/PJAA.87.128zbMath1235.35028OpenAlexW2069673104MaRDI QIDQ665913

Hideo Ueda

Publication date: 7 March 2012

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.87.128

zbMATH Keywords

energyinitial value problemswave equationsresonancesHill's equationcompactly supported initial functioninvisibility phenomenon

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Growth and boundedness of solutions to ordinary differential equations (34C11) Initial value problems for second-order hyperbolic equations (35L15) Resonance in context of PDEs (35B34)

Related Items (4)

Small data wave maps in cyclic spacetime ⋮ Stability on time-dependent domains: convective and dilution effects ⋮ Stability on time-dependent domains ⋮ Problems on time-varying domains: formulation, dynamics, and challenges

Cites Work

• An example of a weakly hyperbolic Cauchy problem not well posed in \(C^\infty\)
• Hyperbolic equations with coefficients rapidly oscillating in time: A result of nonstability
• Note on lower bounds of energy growth for solutions to wave equations
• Smooth localized parametric resonance for wave equations
• Parameteric resonance and nonexistence of the global solution to nonlinear wave equations
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