Quantization of energy and weakly turbulent profiles of solutions to some damped second-order evolution equations

DOI10.1515/anona-2017-0181zbMath1418.35036arXiv1701.08604OpenAlexW2962814900MaRDI QIDQ2417248

Massimo Gobbino, Marina Ghisi, Alain Haraux

Publication date: 12 June 2019

Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.08604

zbMATH Keywords

decay rateweak turbulenceaveraging procedurenonlinear damping termdichotomy phenomenonequipartition of the energy

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order nonlinear hyperbolic equations (35L70) Abstract hyperbolic equations (35L90) Pattern formations in context of PDEs (35B36)

Related Items (6)

Lower bound for the blow-up time for a general nonlinear nonlocal porous medium equation under nonlinear boundary condition ⋮ Upper semicontinuity of pullback attractors for a nonautonomous damped wave equation ⋮ Global existence and asymptotic behaviour of solution for a damped nonlinear hyperbolic equation ⋮ Blow-up of solutions for a wave equation with nonlinear averaged damping and nonlocal nonlinear source terms ⋮ Arbitrarily positive initial energy blowup and blowup time for some fourth-order viscous wave equation ⋮ Energy decay and blow-up of solutions for a viscoelastic equation with nonlocal nonlinear boundary dissipation

Cites Work

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• 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
• \(L^{p}\) estimates of solutions to some non-linear wave equations in one space dimension
• The Convergence Problem for Dissipative Autonomous Systems
• Optimality of Energy Estimates for the Wave Equation with Nonlinear Boundary Velocity Feedbacks

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