Large-time dynamics for a class of KPP-type equations in periodic media

DOI10.1016/j.crma.2008.07.028zbMath1156.35322OpenAlexW1993847936MaRDI QIDQ952118

Michaël Bages, Jean-Michel Roquejoffre, Patrick Martinez

Publication date: 6 November 2008

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2008.07.028

zbMATH Keywords

one space dimensionpulsating wave solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57)

Related Items (9)

Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations ⋮ Convergence to pulsating traveling waves with minimal speed in some KPP heterogeneous problems ⋮ Uniqueness and stability properties of monostable pulsating fronts ⋮ Global stability of critical-speed pulsating fronts for degenerate monostable reactions ⋮ Existence of pulsating waves of advection-reaction-diffusion equations of ignition type by a new method ⋮ Fast propagation for KPP equations with slowly decaying initial conditions ⋮ Large-time dynamics for a class of KPP-type equations in periodic media ⋮ Spreading speeds in slowly oscillating environments ⋮ How travelling waves attract the solutions of KPP-type equations

Cites Work

• Nontrivial large-time behaviour in bistable reaction-diffusion equations
• Large-time dynamics for a class of KPP-type equations in periodic media
• The behavior of solutions of some non-linear diffusion equations for large time
• Long-time behaviour of heat flow: Global estimates and exact asymptotics
• The speed of propagation for KPP type problems. I: Periodic framework
• Qualitative properties of monostable pulsating fronts: Exponential decay and monotonicity
• Convergence of solutions of the Kolmogorov equation to travelling waves
• Space-time behaviour in problems of hydrodynamic type: a case study
• Entire solutions of the KPP equation
• Local stability of critical fronts in nonlinear parabolic partial differential equations
• Front propagation in periodic excitable media

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