How travelling waves attract the solutions of KPP-type equations

DOI10.1090/S0002-9947-2012-05554-1zbMath1284.35108MaRDI QIDQ2841407

Michaël Bages, Patrick Martinez, Jean-Michel Roquejoffre

Publication date: 25 July 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

stabilityCole-Hopf transformationreaction diffusion equationstraveling wavesKolmogorov-Petrovskii-PiskunovKPP equationsattractive properties

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Traveling wave solutions (35C07) Semilinear parabolic equations (35K58)

Related Items (10)

Speed-up of combustion fronts in shear flows ⋮ Nontrivial dynamics beyond the logarithmic shift in two-dimensional Fisher-KPP equations ⋮ Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations ⋮ Admissible speeds of transition fronts for nonautonomous monostable equations ⋮ Existence of multi-dimensional pulsating fronts for KPP equations: a new formulation approach ⋮ Convergence to pulsating traveling waves with minimal speed in some KPP heterogeneous problems ⋮ Planar Propagating Terraces and the Asymptotic One-dimensional Symmetry of Solutions of Semilinear Parabolic Equations ⋮ Existence of pulsating waves of advection-reaction-diffusion equations of ignition type by a new method ⋮ Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on ℝ ⋮ Transition fronts for the Fisher-KPP equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of pulsating waves in a monostable reaction-diffusion system in solid combustion
• Uniqueness and stability properties of monostable pulsating fronts
• Complexity of large time behaviour of evolution equations with bounded data
• Nontrivial large-time behaviour in bistable reaction-diffusion equations
• Traveling fronts in space-time periodic media
• Existence of pulsating waves in a model of flames in sprays
• Large-time dynamics for a class of KPP-type equations in periodic media
• Geometric theory of semilinear parabolic equations
• On the stability of waves of nonlinear parabolic systems
• The behavior of solutions of some non-linear diffusion equations for large time
• Eventual monotonicity and convergence to travelling fronts for the solutions of parabolic equations in cylinders
• Long-time behaviour of heat flow: Global estimates and exact asymptotics
• On bounded and unbounded global solutions of a supercritical semilinear heat equation
• Travelling fronts in cylinders
• On the structure of the spectra of periodic travelling waves
• The rate of attraction of super-critical waves in a Fisher-KPP type model with shear flow
• Qualitative properties of monostable pulsating fronts: Exponential decay and monotonicity
• Irregular behavior of solutions for Fisher's equation
• Convergence of solutions of the Kolmogorov equation to travelling waves
• Generation of Analytic Semigroups by Strongly Elliptic Operators Under General Boundary Conditions
• Space-time behaviour in problems of hydrodynamic type: a case study
• A Parabolic Equation of the KPP Type in Higher Dimensions
• Front propagation in periodic excitable media
• Non-adiabatic KPP fronts with an arbitrary Lewis number
• Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
• Travelling fronts and entire solutions of the Fisher-KPP equation in \({\mathbb R}^N\)

This page was built for publication: How travelling waves attract the solutions of KPP-type equations