Local existence and global nonexistence theorems for a damped nonlinear hyperbolic equation

DOI10.1016/J.JMAA.2010.02.054zbMath1194.35273OpenAlexW2064828109MaRDI QIDQ972457

Shubin Wang, Guowang Chen, Ruili Song

Publication date: 19 May 2010

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.02.054

zbMATH Keywords

contraction mapping principleconcavity methodthree dimensionsinitial boundary value problemlocal solutionblow up of solutionsDamped nonlinear hyperbolic equationsimply supported boundary

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order hyperbolic equations (35L35) Higher-order nonlinear hyperbolic equations (35L75) Blow-up in context of PDEs (35B44)

Related Items (5)

Asymptotic behavior of solutions to a class of fourth-order nonlinear evolution equations with dispersive and dissipative terms ⋮ Asymptotic behavior of solutions to the damped nonlinear hyperbolic equation ⋮ Global existence and asymptotic behaviour of solution for a damped nonlinear hyperbolic equation ⋮ THE BOUNDARY VALUE PROBLEM FOR ONE CLASS OF HIGHER-ORDER SEMILINEAR PARTIAL DIFFERENTIAL EQUATIONS ⋮ Existence and nonexistence of global solutions to the Cauchy problem of the nonlinear hyperbolic equation with damping term

Cites Work

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• The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types
• Global solvability for damped abstract nonlinear hyperbolic systems
• Blow-up of solution of an initial boundary value problem for a damped nonlinear hyperbolic equation.
• Energy decay for a damped nonlinear hyperbolic equation
• A nonlinear beam equation
• The initial-boundary value problems for a class of nonlinear wave equations with damping term

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