Reaction-diffusion waves in an isothermal chemical system with general orders of autocatalysis and spatial dimension

DOI10.1007/BF00948484zbMath0779.35057OpenAlexW1982067095MaRDI QIDQ687421

John H. Merkin, David John Needham

Publication date: 24 October 1993

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

Full work available at URL: https://doi.org/10.1007/bf00948484

zbMATH Keywords

a priori estimatesinitial value problemsimilarity solutionthreshold valueautocatalytic systembehaviour of the solutionreaction- diffusion wavestravelling wave equations

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Classical flows, reactions, etc. in chemistry (92E20)

Related Items (14)

Propagation speeds of traveling fronts for higher order autocatalytic reaction-diffusion systems ⋮ Hair-triggered instability of radial steady states, spread and extinction in semilinear heat equations ⋮ The asymptotic critical wave speed in a family of scalar reaction-diffusion equations ⋮ A geometric analysis of front propagation in a family of degenerate reaction-diffusion equations with cutoff ⋮ Global stability of critical-speed pulsating fronts for degenerate monostable reactions ⋮ Propagation dynamics of degenerate monostable equations in space-time periodic media ⋮ A boundary-driven reaction front ⋮ Gevrey properties of the asymptotic critical wave speed in a family of scalar reaction-diffusion equations ⋮ Existence of traveling waves in a simple isothermal chemical system with the same order for autocatalysis and decay ⋮ Travelling waves in autocatalytic chemical systems with decay: bounds on existence ⋮ Rigorous asymptotic expansions for critical wave speeds in a family of scalar reaction-diffusion equations ⋮ The effect of an electric field on reaction fronts in autocatalytic systems ⋮ Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I: Stability analysis ⋮ The evolution of reaction-diffusion waves in a class of scalar reaction-diffusion equations: algebraic decay rates

Cites Work

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• Techniques of asymptotic analysis
• The Role of Critical Exponents in Blowup Theorems
• A note on the properties of a family of travelling-wave solutions arising in cubic autocatalysis
• The effects of geometrical spreading in two and three dimensions on the formation of travelling wavefronts in a simple, isothermal, chemical system
• The development of travelling waves in a simple isothermal chemical system with general orders of autocatalysis and decay
• On a singular initial-boundary-value problem for a reaction-diffusion equation arising from a simple model of isothermal chemical autocatalysis
• On the existence and uniqueness of solutions to a singular nonlinear boundary value problem arising in isothermal autocatalytic chemical kinetics
• The development of travelling waves in a simple isothermal chemical system - I. Quadratic autocatalysis with linear decay
• The development of travelling waves in a simple isothermal chemical system II. Cubic autocatalysis with quadratic and linear decay
• The development of travelling waves in a simple isothermal chemical system III. Cubic and mixed autocatalysis

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