Global existence and nonexistence of solutions for a viscoelastic wave equation with nonlinear boundary source term

DOI10.1002/mana.201500169zbMath1353.35071OpenAlexW2302182158MaRDI QIDQ2825991

Huafei Di, Xiaoming Peng, Yadong Shang

Publication date: 14 October 2016

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201500169

zbMATH Keywords

invariant setspotential wellsnonlinear boundary source

Mathematics Subject Classification ID

Weak solutions to PDEs (35D30) Pseudohyperbolic equations (35L82) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Blow-up in context of PDEs (35B44) Integro-partial differential equations (35R09)

Related Items (9)

A global nonexistence of solutions for a quasilinear viscoelastic wave equation with acoustic boundary conditions ⋮ Global nonexistence for a viscoelastic wave equation with acoustic boundary conditions ⋮ Invariance and existence analysis of viscoelastic equations with nonlinear damping and source terms on corner singularity ⋮ Global existence, exponential decay and finite time blow-up of solutions for a class of semilinear pseudo-parabolic equations with conical degeneration ⋮ Variable-coefficient viscoelastic wave equation with acoustic boundary conditions: global existence, blowup and energy decay rates ⋮ Dynamics properties for a viscoelastic Kirchhoff-type equation with nonlinear boundary damping and source terms ⋮ Global existence, nonexistence, and decay of solutions for a viscoelastic wave equation with nonlinear boundary damping and source terms ⋮ Unnamed Item ⋮ Global existence and blow-up phenomenon for a quasilinear viscoelastic equation with strong damping and source terms

Cites Work

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• Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations
• Blow-up solutions for a nonlinear wave equation with boundary damping and interior source
• Global nonexistence for a semilinear wave equation with nonlinear boundary dissipation
• On a viscoelastic equation with nonlinear boundary damping and source terms: global existence and decay of the solution
• On decay and blow-up of the solution for a viscoelastic wave equation with boundary damping and source terms
• Blow-up of solutions of a nonlinear viscoelastic wave equation
• Fourth order wave equations with nonlinear strain and source terms
• Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction
• Exponential energy decay of solutions of viscoelastic wave equations
• Blow up of solutions of a nonlinear viscoelastic wave equation
• General decay and blow-up of solution for a quasilinear viscoelastic problem with nonlinear source
• On the control of solutions of viscoelastic equations with boundary feedback
• A global nonexistence theorem for viscoelastic equations with arbitrary positive initial energy
• Saddle points and instability of nonlinear hyperbolic equations
• Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping.
• Existence and uniform decay of the wave equation with nonlinear boundary damping and boundary memory source term
• Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term
• General decay rate estimates for viscoelastic dissipative systems
• Existence and decay of solutions of a viscoelastic equation with a nonlinear source
• Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation
• Asymptotic behavior of solutions to the phase-field equations with Neumann boundary condi\-tions
• Existence and uniform decay for a non-linear viscoelastic equation with strong damping
• A symmetric regularized long-wave equation for shallow water waves
• Evolution and breaking of ion-acoustic waves
• Blow up and global existence in a nonlinear viscoelastic wave equation
• Global well-posedness for strongly damped viscoelastic wave equation
• Global existence and uniform stability of solutions for a quasilinear viscoelastic problem
• General decay of energy for a viscoelastic equation with nonlinear damping

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