Results in Mathematics

, Volume 21, Issue 1–2, pp 200–210 | Cite as

On the Existence of Pulses in Reaction- Diffusion- Equations

  • Klaus R. Schneider
Article
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Abstract

We apply the theory of invariant manifolds for singularly perturbed ordinary differential equations and results about the persistence of homoclinic orbits in autonomous differential systems with several parameters in order to establish the existence of pulses in reaction-diffusion systems. Essential assumptions for the existence of pulses are the following: (i) Existence of a homoclinic orbit to a hyperbolic equilibrium in the corresponding reaction system. (ii) The quotient of some measure for the diffusivities and the square of the puls speed is sufficiently small. (iii) Validity of some transversality condition. The last assumption requires the occurence of parameters in the reaction term.

1980 Mathematics Subject Classification (1985 Revision)

35K57 34C45 34D15 

Keywords and phrases

Reaction-diffusion-system travelling waves pulses invariant manifolds homoclinic orbits singularly perturbed differential equations 
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Copyright information

© Birkhäuser Verlag, Basel 1992

Authors and Affiliations

  • Klaus R. Schneider
    • 1
  1. 1.Institut für Angewandte Analysis und StochastikBerlin

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