Smooth localized parametric resonance for wave equations

DOI10.1515/CRELLE.2008.015zbMath1158.35012MaRDI QIDQ3524787

Jeffrey Rauch, Ferruccio Colombini

Publication date: 15 September 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

zbMATH Keywords

exponentially growing solutiontwo space dimensions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Periodic solutions to ordinary differential equations (34C25) A priori estimates in context of PDEs (35B45) Resonance in context of PDEs (35B34)

Related Items (6)

Note on lower bounds of energy growth for solutions to wave equations ⋮ A remark on parametric resonance for wave equations with a time periodic coefficient ⋮ Some examples causing energy growth for solutions to wave equations ⋮ Cauchy problem for semilinear wave equation with time-dependent metrics ⋮ Localization in the Liouville lattice and movable discrete breathers ⋮ Exponential growth for the wave equation with compact time-periodic positive potential

Cites Work

• Non-uniqueness in hyperbolic Cauchy problems
• Dynamic phase transitions in a van der Waals fluid
• The spectrum of a hyperbolic evolution operator
• Asymptotic behavior for the vibrating string with a moving boundary
• Decay of solutions to nondissipative hyperbolic systems on compact manifolds

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