On the existence of pulses in reaction-diffusion-equations
type: Item
instance of: scholarly article
title: On the existence of pulses in reaction-diffusion-equations
zbMATH Open document ID: 0762.35050
DOI: 10.1007/BF03323079
published in: Results in Mathematics
publication date: 1992-09-27T00:00:00Z
review text: The author applies 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 hyperbolic equilibrium in the corresponding reaction system. (ii) The quotient of some measure for the diffusivities and the square of the pulse speed is sufficiently small. (iii) Validity of some transversality condition. The last assumption requires the occurence of parameters in the reaction term.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 62162
zbMATH Keywords: theory of invariant manifolds
zbMATH Keywords: hyperbolic equilibrium
author: Klaus R. Schneider
reviewed by: Zongyi Hou
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 62162