Propagation in a kinetic reaction-transport equation: travelling waves and accelerating fronts

DOI10.1007/s00205-014-0837-7zbMath1317.35267arXiv1307.8325OpenAlexW2055377239MaRDI QIDQ2354689

Emeric Bouin, Vincent Calvez, Gregoire Nadin

Publication date: 20 July 2015

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.8325

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Cell movement (chemotaxis, etc.) (92C17)

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Cites Work

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• A kinetic eikonal equation
• Modeling the spread of Phytophthora
• Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration
• Fractional diffusion limit for collisional kinetic equations
• Models of dispersal in biological systems
• Traveling bands of chemotactic bacteria: a theoretical analysis
• Front propagation in Fisher-KPP equations with fractional diffusion
• Biased random walk models for chemotaxis and related diffusion approximations
• On the nonlinear dynamics of travelling fronts
• Stability of travelling waves for a damped hyperbolic equation
• Spreading disease: Integro-differential equations old and new.
• Travelling fronts for multidimensional nonlinear transport equations
• Limit sets for multidimensional nonlinear transport equations
• Kinetic models for chemotaxis and their drift-diffusion limits
• Fast propagation for KPP equations with slowly decaying initial conditions
• The influence of fractional diffusion in Fisher-KPP equations
• General relative entropy inequality: an illustration on growth models
• Accelerating Solutions in Integro-Differential Equations
• Hyperbolic travelling fronts
• Local stability of critical fronts in nonlinear parabolic partial differential equations
• The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes
• From Individual to Collective Behavior in Bacterial Chemotaxis
• Transition Between Linear and Exponential Propagation in Fisher-KPP Type Reaction-Diffusion Equations
• Traveling Waves of a Kinetic Transport Model for the KPP-Fisher Equation
• Hyperbolic traveling waves driven by growth

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