A blow-up result for a higher-order nonlinear Kirchhoff-type hyperbolic equation

DOI10.1016/j.aml.2006.08.018zbMath1132.35420OpenAlexW2092438777MaRDI QIDQ2470552

Belkacem Said-Houari, Messaoudi A. Salim

Publication date: 14 February 2008

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

Full work available at URL: https://doi.org/10.1016/j.aml.2006.08.018

zbMATH Keywords

Dirichlet boundary conditionsblow-uphyperbolicpositive initial energyhigher orderKirchhoffarbitrary space dimension

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Higher-order nonlinear hyperbolic equations (35L75)

Related Items (16)

Existence, decay, and blow-up of solutions for a higher-order Kirchhoff-type equation with delay term ⋮ LIFESPAN ESTIMATES FOR SOLUTIONS OF POLYHARMONIC KIRCHHOFF SYSTEMS ⋮ The family of random attractors for nonautonomous stochastic higher-order Kirchhoff equations with variable coefficients ⋮ Unnamed Item ⋮ Blow-up of solutions to a class of Kirchhoff equations with strong damping and nonlinear dissipation ⋮ Global existence and blowup of solutions for a class of nonlinear higher-order wave equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation ⋮ Global nonexistence for abstract evolution equations with dissipation ⋮ Blow up solutions to a system of higher-order Kirchhoff-type equations with positive initial energy ⋮ Blow-up of solutions for a system of higher-order nonlinear Kirchhoff-type equations ⋮ Global existence and energy decay estimate of solutions for a higher-order Kirchhoff type equation with damping and source term ⋮ A blow-up result for Kirchhoff-type equations with high energy ⋮ Blow-up results for a nonlinear hyperbolic equation with Lewis function

Cites Work

• Unnamed Item
• Decay estimates for some semilinear damped hyperbolic problems
• The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types
• Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation
• Existence of a solution of the wave equation with nonlinear damping and source terms
• Global nonexistence theorems for quasilinear evolution equations with dissipation
• On global solutions and blow-up solutions of nonlinear Kirchhoff strings with nonlinear dissipation
• Development of singularities in solutions of a hyperbolic system
• Blowup of solutions of a nonlinear wave equation
• Global existence and blowup of solutions for a higher-order Kirchhoff-type equation with nonlinear dissipation.
• Global nonexistence theorems for a class of evolution equations with dissipation
• On Global Existence, Asymptotic Stability and Blowing Up of Solutions for Some Degenerate Non-linear Wave Equations of Kirchhoff Type with a Strong Dissipation
• Global non-existence of solutions of a class of wave equations with non-linear damping and source terms
• REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NONLINEAR EVOLUTION EQUATIONS
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Blow-up of solutions for the Kirchhoff equation of q-Laplacian type with nonlinear dissipation
• Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave Equations

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