Hostname: page-component-669899f699-rg895 Total loading time: 0 Render date: 2025-04-26T09:10:36.482Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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