Global stability of travelling fronts for a damped wave equation with bistable nonlinearity

DOI10.24033/asens.2091zbMath1169.35041arXiv0710.0794OpenAlexW2951643142MaRDI QIDQ3632714

Romain Joly, Thierry Gallay

Publication date: 12 June 2009

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.0794

zbMATH Keywords

Lyapunov functionglobal stabilitydamped wave equationtravelling front

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Stability in context of PDEs (35B35) Maximum principles in context of PDEs (35B50) Second-order nonlinear hyperbolic equations (35L70)

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Slow motion for one-dimensional nonlinear damped hyperbolic Allen-Cahn systems ⋮ Computation and Stability of Traveling Waves in Second Order Evolution Equations ⋮ Global stability of travelling fronts for a damped wave equation ⋮ A variational approach to reaction-diffusion equations with forced speed in dimension 1 ⋮ Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure ⋮ Hyperbolic traveling waves driven by growth ⋮ Extremal equilibria for monotone semigroups in ordered spaces with application to evolutionary equations ⋮ Analytical and numerical investigation of traveling waves for the Allen–Cahn model with relaxation ⋮ Exponential decay for the damped wave equation in unbounded domains ⋮ Computation and stability of waves in equivariant evolution equations ⋮ Control of reaction-diffusion models in biology and social sciences

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