Sharp lifespan estimates of blowup solutions to semi-linear wave equations with time-dependent effective damping

DOI10.1142/S0219891619500176zbMath1445.35250arXiv1808.06189WikidataQ127003223 ScholiaQ127003223MaRDI QIDQ5108361

Motohiro Sobajima, Masahiro Ikeda, Yuta Wakasugi

Publication date: 4 May 2020

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.06189

zbMATH Keywords

wave equationtime-dependent dampingtest-function methodlifespan of solutionssmall data blowup

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Blow-up in context of PDEs (35B44) Second-order semilinear hyperbolic equations (35L71)

Related Items (15)

Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass ⋮ Higher-order asymptotic expansion for abstract linear second-order differential equations with time-dependent coefficients ⋮ Blow-up of solutions of semilinear wave equations in accelerated expanding Friedmann–Lemaître–Robertson–Walker spacetime ⋮ Lifespan of classical solutions to one dimensional fully nonlinear wave equations with time-dependent damping ⋮ Strauss exponent for semilinear wave equations with scattering space dependent damping ⋮ Weighted energy method for semilinear wave equations with time-dependent damping ⋮ Lifespan estimates of solutions to semilinear wave equations with damping term on the exterior domain ⋮ Life-Span of Classical Solutions to a Semilinear Wave Equation with Time-Dependent Damping ⋮ Critical exponent for the wave equation with a time-dependent scale invariant damping and a cubic convolution ⋮ Unnamed Item ⋮ Critical exponent for the semilinear wave equations with a damping increasing in the far field ⋮ Blow up of solutions of semilinear wave equations in Friedmann–Lemaître–Robertson–Walker spacetime ⋮ On heatlike lifespan of solutions of semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime ⋮ Global existence for semilinear wave equations with scaling invariant damping in 3-D ⋮ Blow-up of solutions to semilinear wave equations with a scaling invariant critical damping

Cites Work

• Lifespan of solutions to the damped wave equation with a critical nonlinearity
• Scaling variables and asymptotic profiles for the semilinear damped wave equation with variable coefficients
• Semi-linear wave equations with effective damping
• A shift in the strauss exponent for semilinear wave equations with a not effective damping
• The sharp estimate of the lifespan for semilinear wave equation with time-dependent damping.
• Blow-up for semilinear damped wave equations with subcritical exponent in the scattering case
• Wave equations with time-dependent dissipation. I: Non-effective dissipation
• Wave equations with time-dependent dissipation. II: Effective dissipation
• Scattering and modified scattering for abstract wave equations with time-dependent dissipation
• Scaling variables and asymptotic expansions in damped wave equations
• Breakdown of solutions to \(\square u+u_ t=| u| ^{1+\alpha}\)
• Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data
• The sharp lifespan estimate for semilinear damped wave equation with Fujita critical power in higher dimensions
• Critical exponent for the semilinear wave equation with time-dependent damping
• Sharp upper bound for lifespan of solutions to some critical semilinear parabolic, dispersive and hyperbolic equations via a test function method
• Solution representations for a wave equation with weak dissipation
• Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case
• Estimates of Lifespan and Blow-up Rates for the Wave Equation with a Time-dependent Damping and a Power-type Nonlinearity
• The threshold of effective damping for semilinear wave equations
• A note on the lifespan of solutions to the semilinear damped wave equation
• A modified test function method for damped waves
• Critical exponent for a nonlinear wave equation with damping
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• Unnamed Item
• Unnamed Item

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