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Directional wave fronts of reaction-diffusion systems

Published online by Cambridge University Press:  17 April 2009

J. Sabina
J. Sabina
Affiliation:
Dpto. de Ecuaciones Funcionales, Facultad de Matemáticas, U. Complutense, 28040-Madrid Dpto. de Matemáticas I, ETSI de Telecomunicación, U. Politecnica de Madrid, 28040-Madrid
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Abstract

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In this work, we study types of undulatory solutions, that we term Directional Wave Fronts (DWF), of non scalar reaction diffusion systems. The DWFs are a natural extension of the well known Plane Wave Fronts (PWFs) solutions. However, the DWFs admit a certain type of boundary conditions. In the present work we show, under suitable conditions on the reaction term, that DWFs also exhibit typical behaviour of PWFs: we just prove the existence of heteroclinic, homoclinic and periodic families of DWFs. Essentially, we require the reaction term to be linearly uncoupled. These results are the generalization of a previous work, concerning the scalar case.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 1 , February 1986 , pp. 1 - 20
Copyright
Copyright © Australian Mathematical Society 1986

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