A geometric analysis of front propagation in a family of degenerate reaction-diffusion equations with cutoff

DOI10.1007/s00033-011-0115-6zbMath1261.35036OpenAlexW2066980874MaRDI QIDQ1938439

Nikola Popović

Publication date: 4 February 2013

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://www.pure.ed.ac.uk/ws/files/10947550/A_geometric_analysis_of_front_propagation_in_a_family_of_degenerate_reaction_diffusion_equations_with_cutoff.pdf

zbMATH Keywords

geometric desingularizationfront speedZeldovich equationdegenerate polynomial potentialHeaviside cutoff

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Initial value problems for second-order parabolic equations (35K15) Traveling wave solutions (35C07) Semilinear parabolic equations (35K58)

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When does colonisation of a semi-arid hillslope generate vegetation patterns? ⋮ Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations ⋮ Shift in the speed of reaction–diffusion equation with a cut-off: Pushed and bistable fronts ⋮ Rigorous results for the minimal speed of Kolmogorov–Petrovskii–Piscounov monotonic fronts with a cutoff ⋮ Wave speeds for the FKPP equation with enhancements of the reaction function

Cites Work

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• A geometric approach to bistable front propagation in scalar reaction-diffusion equations with cut-off
• Reaction-diffusion waves in an isothermal chemical system with general orders of autocatalysis and spatial dimension
• The asymptotic critical wave speed in a family of scalar reaction-diffusion equations
• Matched asymptotic expansions. Ideas and techniques
• Front propagation into unstable states
• Asymptotic expansions using blow-up
• Ordinary differential equations. An introduction to nonlinear analysis. Transl. from the German by Gerhard Metzen
• Rigorous asymptotic expansions for Lagerstrom's model equation -- a geometric approach
• Travelling waves in nonlinear diffusion-convection reaction
• Travelling wave phenomena in some degenerate reaction-diffusion equations
• Variational characterization of the speed of propagation of fronts for the nonlinear diffusion equation
• Rigorous asymptotic expansions for critical wave speeds in a family of scalar reaction-diffusion equations
• Qualitative theory of planar differential systems
• Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
• The critical wave speed for the Fisher–Kolmogorov–Petrowskii–Piscounov equation with cut-off
• A note on the properties of a family of travelling-wave solutions arising in cubic autocatalysis
• Reaction-diffusion and phase waves occurring in a class of scalar reaction-diffusion equations
• The effects of variable diffusivity on the development of travelling waves in a class of reaction-diffusion equations
• Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms
• Algebraic decay and variable speeds in wavefront solutions of a scalar reaction-diffusion equation
• Invariant manifolds
• Critical wave speeds for a family of scalar reaction-diffusion equations

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