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Continuous and semidiscrete travelling waves for a phase relaxation model. (English) Zbl 0812.35166

Summary: 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.

MSC:

35R35 Free boundary problems for PDEs
35A35 Theoretical approximation in context of PDEs
35Q35 PDEs in connection with fluid mechanics
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[1] DOI: 10.1093/imamat/34.3.225 · Zbl 0585.35053
[2] DOI: 10.1007/BF01398688 · Zbl 0617.65125
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[7] Nochetto, Variational and Free Boundary Problems (1992)
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