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.

Continuous and semidiscrete travelling waves for a phase relaxation model / R.H. Nochetto, M. Paolini, C. Verdi. - In: EUROPEAN JOURNAL OF APPLIED MATHEMATICS. - ISSN 0956-7925. - 5:2(1994), pp. 177-199. [10.1017/S095679250000139X]

Continuous and semidiscrete travelling waves for a phase relaxation model

C. Verdi
Ultimo
1994

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.
Settore MAT/08 - Analisi Numerica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/187298
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