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

  • J. H. Merkin
  • D. J. Needham
Original Papers

Abstract

The possibility of initiating reaction-diffusion waves in an autocatalytic system represented schematically byA→B, ratekab p (p >- 1, witha, b being the concentrations ofA andB respectively) is considered through the local input ofB, measured by the parameter β0, into an otherwise uniform expanse ofA. It is shown that for 1 <-p < 1 + (2/N) (whereN is the space dimension) waves develop no matter how small the value of β0, while forp > 1 + (2/N) there is some threshold value of β0 below which waves are not formed, with diffusion playing the dominant role throughout. A lower bound for this threshold value is found. The permanent-form travelling wave equations are then discussed and the behaviour of the solution asp → 1 is considered in detail. It is shown that a three-region structure develops with the asymptotic wave speedv being singular (of the formv ∼ 2−2.3381 (p- 1)2/3) asp → 1.

Keywords

Wave Equation Mathematical Method Dominant Role Spatial Dimension Space Dimension 

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Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • J. H. Merkin
    • 1
  • D. J. Needham
    • 2
  1. 1.Dept of Applied MathematicsUniversity of LeedsLeeds
  2. 2.School of MathematicsUniversity of East AngliaNorwichUK

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