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Continuous and semidiscrete travelling waves for a phase relaxation model

Published online by Cambridge University Press:  26 September 2008

Ricardo H. Nochetto ,
Maurizio Paolini  and
Claudio Verdi
Ricardo H. Nochetto
Affiliation:
Department of Mathematics and Institute of Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
Maurizio Paolini
Affiliation:
Dipartimento di Matemalica, Università di Milano, Via Saldini 50, 20133 Milano, and Istituto di Analisi Numerica del CNR, Corso Carlo Alberto 5, 21700 Pavia, Italy
Claudio Verdi
Affiliation:
Dipartimento di Matemalica, Università di Milano, Via Saldini 50, 20133 Milano, and Istituto di Analisi Numerica del CNR, Corso Carlo Alberto 5, 21700 Pavia, Italy
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Abstract

Quite precise asymptotic estimates, in terms of the relaxation parameter and the time step, are derived for travelling wave solutions to a Stefan problem with phase relaxation and a semidiscrete counterpart. These estimates quantify the regularizing effects of phase relaxation and time discretization that give rise to thin transition layers as opposed to sharp interfaces. Layer width estimates, pointwise error estimates, and asymptotic expressions for the profile of the relevant physical variables are proved. Applications to a related nonlinear Chernoff formula are also given.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 5 , Issue 2 , June 1994 , pp. 177 - 199
Copyright
Copyright © Cambridge University Press 1994

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References

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