Parameteric resonance and nonexistence of the global solution to nonlinear wave equations

DOI10.1006/JMAA.2000.7469zbMath0983.35087OpenAlexW2032818613MaRDI QIDQ5944920

Karen Yagdjian

Publication date: 9 April 2002

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

Full work available at URL: https://doi.org/10.1006/jmaa.2000.7469

zbMATH Keywords

small initial datablowing up solution

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (9)

On asymptotic behavior of solution to a nonlinear wave equation with Space-time speed of propagation and damping terms ⋮ Decay estimates for a Klein-Gordon model with time-periodic coefficients ⋮ Small data wave maps in cyclic spacetime ⋮ Small data blow-up for a system of nonlinear Schrödinger equations ⋮ \(C^m\)-theory of damped wave equations with stabilisation ⋮ A remark on parametric resonance for wave equations with a time periodic coefficient ⋮ Lp - Lq Decay Estimates for Wave Equations with Time-Dependent Coefficients ⋮ The influence of oscillations on global existence for a class of semi-linear wave equations ⋮ About the solvability behaviour for special classes of nonlinear hyperbolic equations

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