Sharpness on the lower bound of the lifespan of solutions to nonlinear wave equations

DOI10.1007/s11401-011-0652-5zbMath1302.35262OpenAlexW1981741963MaRDI QIDQ741433

Yi Zhou, Wei Han

Publication date: 12 September 2014

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-011-0652-5

zbMATH Keywords

Cauchy problemnonlinear wave equationsmall initial datalifespan

Mathematics Subject Classification ID

Initial value problems for second-order hyperbolic equations (35L15) Blow-up in context of PDEs (35B44) Second-order semilinear hyperbolic equations (35L71)

Related Items (12)

Linear tracking-differentiator and application to online estimation of the frequency of a sinusoidal signal with random noise perturbation ⋮ Global existence for semilinear wave equations with the critical blow-up term in high dimensions ⋮ Lifespan of solutions to the damped wave equation with a critical nonlinearity ⋮ Life-span of classical solutions to two dimensional fully nonlinear wave equations ⋮ Lifespan of classical solutions to one dimensional fully nonlinear wave equations with time-dependent damping ⋮ Almost global solutions of semilinear wave equations with the critical exponent in high dimensions ⋮ Life-Span of Classical Solutions to a Semilinear Wave Equation with Time-Dependent Damping ⋮ The Lifespan of Smooth Solutions to Semilinear Wave Equations in Schwarzschild Space-Time ⋮ Life-span of classical solutions to one dimensional initial-boundary value problems for general quasilinear wave equations ⋮ Blowup of smooth solutions of a class of complex conservation laws ⋮ The sharp upper bound of the lifespan of solutions to critical semilinear wave equations in high dimensions ⋮ Blow Up for Some Semilinear Wave Equations in Multi-space Dimensions

Cites Work

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• Nonexistence of global solutions to semilinear wave equations in high dimensions
• Blow-up for nonlinear wave equations with slowly decaying data
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Life–span of classocal solutions to fully nonlinear wave equations
• Long-time existence for small amplitude semilinear wave equations
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
• Blow up of solutions to the Cauchy problem for nonlinear wave equations

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