Transition Between Linear and Exponential Propagation in Fisher-KPP Type Reaction-Diffusion Equations

DOI10.1080/03605302.2012.718024zbMath1263.35142arXiv1111.0408OpenAlexW2083765731MaRDI QIDQ4902757

Anne-Charline Coulon, Jean-Michel Roquejoffre

Publication date: 17 January 2013

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.0408

zbMATH Keywords

fundamental solutionreaction-diffusioncompactly supported initial datafractional diffusion

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Fundamental solutions to PDEs (35A08) Fractional partial differential equations (35R11)

Related Items (13)

Non-local competition slows down front acceleration during dispersal evolution ⋮ Mesoscopic models in biology ⋮ The effect of a line with nonlocal diffusion on Fisher-KPP propagation ⋮ Super-linear spreading in local and non-local cane toads equations ⋮ Super-linear spreading in local bistable cane toads equations ⋮ Acceleration of propagation in a chemotaxis‐growth system with slowly decaying initial data ⋮ Large‐scale asymptotics of velocity‐jump processes and nonlocal Hamilton–Jacobi equations ⋮ The KPP-problem and \(\log t\)-front shift for higher-order semilinear parabolic equations ⋮ Fast propagation for reaction-diffusion cooperative systems ⋮ Accelerated front propagation for monostable equations with nonlocal diffusion: multidimensional case ⋮ Nonlocal dispersal cooperative systems: acceleration propagation among species ⋮ Singular Limits for Reaction-Diffusion Equations with Fractional Laplacian and Local or Nonlocal Nonlinearity ⋮ Propagation in a kinetic reaction-transport equation: travelling waves and accelerating fronts

Cites Work

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• The periodic patch model for population dynamics with fractional diffusion
• Front propagation in Fisher-KPP equations with fractional diffusion
• Multidimensional nonlinear diffusion arising in population genetics
• Front propagation in reactive systems with anomalous diffusion
• The speed of propagation for KPP type problems. I: Periodic framework
• On spreading speeds and traveling waves for growth and migration models in a periodic habitat
• Fast propagation for KPP equations with slowly decaying initial conditions
• Accelerating Solutions in Integro-Differential Equations
• The speed of propagation for KPP type problems. II: General domains
• Symmetric Stable Laws and Stable-Like Jump-Diffusions

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