Existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping

DOI10.1016/j.na.2006.04.012zbMath1129.35046OpenAlexW2048935381MaRDI QIDQ876965

Mingxin Wang, Fuqin Sun

Publication date: 19 April 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.04.012

zbMATH Keywords

decay estimatespositive average value

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Higher-order hyperbolic systems (35L55) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (30)

A remark on the blowing up of solutions to Nakao's problem ⋮ Blow-up of solutions to Nakao's problem via an iteration argument ⋮ A general nonexistence result for inhomogeneous semilinear wave equations with double damping and potential terms ⋮ Critical curve for a weakly coupled system of semilinear \(\sigma\)-evolution equations with frictional damping ⋮ Existence and blow-up of solutions for damped ave system with nonlinear memory ⋮ Global existence and nonexistence results for a class of semilinear hyperbolic systems ⋮ The critical exponent for the dissipative plate equation with power nonlinearity ⋮ Damped wave equation with a critical nonlinearity in higher space dimensions ⋮ Weakly coupled systems of semilinear effectively damped waves with time-dependent coefficient, different power nonlinearities and different regularity of the data ⋮ Global existence of solutions for weakly coupled systems of semi-linear structurally damped σ-evolution models ⋮ The Cauchy problem for the nonlinear damped wave equation with slowly decaying data ⋮ Unnamed Item ⋮ Well-posedness and exponential decay for a porous thermoelastic system with second sound and a time-varying delay term in the internal feedback ⋮ Existence of global solutions for a weakly coupled system of semilinear viscoelastic damped \(\sigma\)-evolution equations ⋮ Weakly coupled system of semilinear wave equations with distinct scale-invariant terms in the linear part ⋮ Global Small data Solutions for a system of semilinear heat equations and the corresponding system of damped wave equations with nonlinear memory ⋮ Blow-up and lifespan estimates for solutions to the weakly coupled system of nonlinear damped wave equations outside a ball ⋮ Large time behavior of solutions for a nonlinear damped wave equation ⋮ Asymptotic behavior of solutions for a system of semilinear heat equations and the corresponding damped wave system ⋮ Sharp lifespan estimates for the weakly coupled system of semilinear damped wave equations in the critical case ⋮ Large time behavior of solutions for a system of nonlinear damped wave equations ⋮ Nonexistence of global solutions for a nonlocal nonlinear hyperbolic system with linear damping ⋮ Nonexistence of global solutions for a class of nonlocal in time and space nonlinear evolution equations ⋮ On the benefit of different additional regularity for the weakly coupled systems of semilinear effectively damped waves ⋮ Critical exponent for the Cauchy problem to the weakly coupled damped wave system ⋮ Results of nonexistence of solutions for some nonlinear evolution problems ⋮ The interplay of critical regularity of nonlinearities in a weakly coupled system of semi-linear damped wave equations ⋮ Global existence and nonexistence of solutions for a system of nonlinear damped wave equations ⋮ Remark on a weakly coupled system of nonlinear damped wave equations ⋮ Global existence of solutions for a weakly coupled system of semilinear damped wave equations

Cites Work

• Unnamed Item
• Existence and non-existence of global solutions for a semilinear heat equation
• Boundedness and blow up for a semilinear reaction-diffusion system
• Finite dimensional exponential attractors for semilinear wave equations with damping
• Global nonexistence for abstract evolution equations with positive initial energy
• Existence of global solutions to the Cauchy problem for the semilinear dissipative wave equations
• Breakdown of solutions to \(\square u+u_ t=| u| ^{1+\alpha}\)
• Asymptotic behavior of solutions of quasilinear hyperbolic equations with linear damping
• Global nonexistence theorems for quasilinear evolution equations with dissipation
• The \(L^{p}\)--\(L^{q}\) estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media
• \(L^p\)-\(L^q\) estimates of solutions to the damped wave equation in 3-dimensional space and their application
• A singular perturbed problem for semilinear wave equations with small parameter
• Local and global existence of solutions to semilinear parabolic initial value problems
• Critical exponents for semilinear dissipative wave equations in \({\mathbb{R}}^N\)
• Global existence and asymptotic behavior of small solutions for semilinear dissipative wave equations
• Long-time asymptotic expansion for the damped semilinear wave equation.
• On the decay property of solutions to the Cauchy problem of the semilinear wave equation with a dissipative term
• On the dynamics of semilinear damped wave equations on
• Finite energy travelling waves for nonlinear damped wave equations
• Fujita’s Exponent for a Semilinear Wave Equation with Linear Damping
• Some remarks on the wave equations with nonlinear damping and source terms
• Critical exponent for a nonlinear wave equation with damping

This page was built for publication: Existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping