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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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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