Global existence and decay of solutions of a nonlinear system of wave equations

DOI10.1080/00036811.2010.549475zbMath1246.35039OpenAlexW2014754642WikidataQ58301894 ScholiaQ58301894MaRDI QIDQ2883293

Belkacem Said-Houari

Publication date: 11 May 2012

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2010.549475

zbMATH Keywords

system of two wave equationsnonlinear damping and source

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order semilinear hyperbolic equations (35L71) Initial-boundary value problems for second-order hyperbolic systems (35L53)

Related Items

Blow up and asymptotic behavior in a nondissipative nonlinear wave equation ⋮ Asymptotic analysis and upper semicontinuity to a system of coupled nonlinear wave equations ⋮ Uniform decay and blow-up of solutions for coupled nonlinear Klein-Gordon equations with nonlinear damping terms ⋮ General decay of solutions of a nonlinear system of viscoelastic wave equations ⋮ Global solutions and blow-up for a class of strongly damped wave equations systems ⋮ On decay and blow-up of solutions for a system of nonlinear wave equations ⋮ General decay of solutions for a nonlinear system of viscoelastic wave equations with degenerate damping and source terms ⋮ Blow up of positive initial-energy solutions for coupled nonlinear wave equations with degenerate damping and source terms ⋮ Global well-posedness for a class of Kirchhoff-type wave system ⋮ Unnamed Item ⋮ Global existence and non-existence analyses to a nonlinear Klein-Gordon system with damping terms under positive initial energy ⋮ Nonexistence of global weak solutions of a system of nonlinear wave equations with nonlinear fractional damping ⋮ Well-posedness and a blow up result for a fractionally damped coupled system

Cites Work

• Unnamed Item
• On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms
• Decay estimates for some semilinear damped hyperbolic problems
• Asymptotic stability of the bounded or almost periodic solution of the wave equation with nonlinear dissipative term
• 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
• Qualitative analysis of a nonlinear wave equation
• Blow up for nonlinear dissipative wave equations in \(\mathbb R^n\)
• Global nonexistence theorems for a class of evolution equations with dissipation
• Stable and unstable sets for the Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms
• Global solutions and finite time blow up for damped semilinear wave equations
• 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
• Blow up of solutions of the Cauchy problem for a wave equation with nonlinear damping and source terms and positive initial energy
• Existence and asymptotic behaviour of solutions for a class of quasi-linear evolution equations with non-linear damping and source terms
• Some remarks on the wave equations with nonlinear damping and source terms
• Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave Equations

This page was built for publication: Global existence and decay of solutions of a nonlinear system of wave equations