Lower bound for the lifespan of solutions for a class of fourth order wave equations

DOI10.1016/j.aml.2015.06.016zbMath1330.35265OpenAlexW782447728MaRDI QIDQ894417

G. A. Philippin, Stella Vernier Piro

Publication date: 30 November 2015

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2015.06.016

zbMATH Keywords

semilinear Petrovsky equations

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order hyperbolic equations (35L35) Blow-up in context of PDEs (35B44) Higher-order semilinear hyperbolic equations (35L76)

Related Items (12)

Exact thresholds for global existence to the nonlinear beam equations with and without a damping ⋮ On decay and blow-up of solutions for a nonlinear Petrovsky system with conical degeneration ⋮ A note on a class of 4th order hyperbolic problems with weak and strong damping and superlinear source term ⋮ Von Karman thermoelastic plates: existence and nonexistence of global solutions ⋮ Arbitrary initial energy blow up for fourth-order viscous damped wave equation with exponential-type growth nonlinearity ⋮ Lower and upper bounds for the blow-up time of a class of damped fourth-order nonlinear evolution equations ⋮ An explicit lower bound for blow up time in a class of nonlinear wave equations with nonlinear damping and source terms ⋮ Blow up of solutions for a nonlinear Petrovsky type equation with time-dependent coefficients ⋮ Bounds for the lifespan of solutions to fourth-order hyperbolic equations with initial data at arbitrary energy level ⋮ Lower bounds for the blow-up time to a nonlinear viscoelastic wave equation with strong damping ⋮ Lifespan for solutions to 4-th order hyperbolic systems with time dependent coefficients ⋮ Existence and nonexistence of global solutions to the Cauchy problem of the nonlinear hyperbolic equation with damping term

Cites Work

• Unnamed Item
• Global nonexistence for a semilinear Petrovsky equation
• Lower bounds for blow-up time in a class of nonlinear wave equations
• A blow up result for a nonlinear wave equation with damping and vanishing initial energy in \(\mathbb R^N\)
• Blow-up phenomena for a class of fourth-order parabolic problems
• Global existence and nonexistence for a nonlinear wave equation with damping and source terms
• Global existence and nonexistence in a system of Petrovsky

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