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Travelling wave solutions of a reaction—infiltration problem and a related free boundary problem

Published online by Cambridge University Press:  26 September 2008

John Chadam ,
Xinfu Chen ,
Elena Comparini  and
Riccardo Ricci
John Chadam
Affiliation:
The Fields Institute, 185 Columbia Street West, Waterloo, Ontario, Canada N2L 5Z5
Xinfu Chen
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
Elena Comparini
Affiliation:
Dipartimento di Matematica “Ulisse Dini”, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
Riccardo Ricci
Affiliation:
Dipartimento di Matematica “F. Enriques”, Università di Milano, Via C. Saldini 50, 20133 Milano, Italy
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Abstract

We consider travelling wave solutions of a reaction–diffusion system arising in a model for infiltration with changing porosity due to reaction. We show that the travelling wave solution exists, and is unique modulo translations. A small parameter ε appears in this problem. The formal limit as ε → 0 is a free boundary problem. We show that the solution for ε > 0 tends, in a suitable norm, to the solution of the formal limit.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 5 , Issue 3 , September 1994 , pp. 255 - 265
Copyright
Copyright © Cambridge University Press 1994

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References

Berestycki, H., Nicolaenko, B. & Schurer, B. 1985 Traveling wave solutions to combustion models and their singular limits. SIAM J. Math. Anal. 16, 1207–1242.CrossRefGoogle Scholar
Chadam, J., Hoff, D., Merino, E., Ortoleva, P. & Sen, A. 1987 Reactive Infiltration Instabilities. IMA J. Appl. Math. 36, 207–220.CrossRefGoogle Scholar
Chadam, J., Ortoleva, P. & Sen, A. 1988 A weakly nonlinear stability analysis of the reactive infiltration interface. SIAM J. Appl. Math. 48, 1362–1378.CrossRefGoogle Scholar
Guckenheimer, J. & Holmes, P. 1986 Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Appl. Math. Sciences 42, Springer-Verlag, New York.Google Scholar
Nochetto, R. H., Paolini, M. & Verdi, C. Continuous and semidiscrete travelling waves for a phase relaxation model. Preprint.Google Scholar