A convergence result for a Stefan problem with phase relaxation

Vincenzo Recupero

doi:10.3934/dcdss.2023119

Article Contents

2023, Volume 16, Issue 12: 3535-3551. Doi: 10.3934/dcdss.2023119

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A convergence result for a Stefan problem with phase relaxation

Vincenzo Recupero

Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy

Dedicated to Pierluigi Colli on the occasion of his 65^th birthday

Received: March 2023

Revised: June 2023

Early access: June 2023

Published: December 2023

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Abstract

In this paper we consider the model of phase relaxation introduced in [22], where an asymptotic analysis is performed toward an integral formulation of the Stefan problem when the relaxation parameter approaches zero. Assuming the natural physical assumption that the initial condition of the phase is constrained, but taking more general boundary conditions, we prove that the solution of this relaxed model converges in a stronger way to the solution of the classical weak Stefan problem.

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Mathematics Subject Classification: 35R35, 35K61, 80A22, 80M30, 80M35.

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References

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