International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 2, Pages 169-193
Existence of reaction-diffusion-convection waves in unbounded strips
1Laboratoire de Mathématiques Appliquées, UMR 5585 CNRS, Université Lyon 1, Villeurbanne 69622, France
2Institute of Fundamental Technological Research, Świetokrzyska 21, Warsaw 00-049, Poland
Received 30 May 2004; Revised 23 November 2004
Copyright © 2005 M. Belk et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Existence of reaction-diffusion-convection waves in unbounded strips is proved in the case of small Rayleigh numbers. In the bistable case the wave is unique, in the monostable case they exist for all speeds greater than the minimal one.
The proof uses the implicit function theorem. Its application is based on the Fredholm property, index, and solvability conditions for elliptic problems in unbounded domains.