Life-Span of Classical Solutions to a Semilinear Wave Equation with Time-Dependent Damping

DOI10.4208/jpde.v36.n3.1OpenAlexW4385815383MaRDI QIDQ6141748

Changwang Xiao, Fei Guo, Jinling Liang

Publication date: 23 January 2024

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

Full work available at URL: https://doi.org/10.4208/jpde.v36.n3.1

zbMATH Keywords

semilinear wave equationlife-spantime-dependent dampingglobal iteration method

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) Classical solutions to PDEs (35A09)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The sharp upper bound of the lifespan of solutions to critical semilinear wave equations in high dimensions
• Sharpness on the lower bound of the lifespan of solutions to nonlinear wave equations
• Wave equations with time-dependent dissipation. I: Non-effective dissipation
• Wave equations with time-dependent dissipation. II: Effective dissipation
• Life-span of classical solutions to one dimensional nonlinear wave equations
• Life span of classical solutions to \(u_{tt} - u_{xx} =| u|^{1+\alpha}\)
• Life span of classical solutions to \(\square u = | u | ^ p\) in two space dimensions
• Breakdown of solutions to \(\square u+u_ t=| u| ^{1+\alpha}\)
• Critical exponent for the semilinear wave equation with time-dependent damping
• Life-span of classical solutions to nonlinear wave equations in two space dimensions
• \( L^1 \) estimates for oscillating integrals and their applications to semi-linear models with \( \sigma \)-evolution like structural damping
• Finite time blow up for critical wave equations in high dimensions
• Blow-up theorems for nonlinear wave equations
• On the Strauss index of semilinear Tricomi equation
• Initial value problems for nonlinear wave equations
• Life–span of classocal solutions to fully nonlinear wave equations
• Solution representations for a wave equation with weak dissipation
• A note on the life-span of classical solutions to nonlinear wave equations in four space dimensions
• Sharp lifespan estimates of blowup solutions to semi-linear wave equations with time-dependent effective damping
• Life-Span of Solutions to Critical Semilinear Wave Equations
• Blow up of solutions to the Cauchy problem for nonlinear wave equations
• Critical exponent for a nonlinear wave equation with damping

This page was built for publication: Life-Span of Classical Solutions to a Semilinear Wave Equation with Time-Dependent Damping