Regularity of the solution to a nonstandard system of phase field\n equations

2013/03/13 by Pierluigi Colli, Colli, Pierluigi, Gianni Gilardi +3
Materials Science · #35A02 #35D10 #35K61 #Analysis of PDEs (math.AP) #FOS: Mathematics #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.1303.3107

openalex publication_date 2013/03/13 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

A nonstandard system of differential equations describing two-species phase\nsegregation is considered. This system naturally arises in the asymptotic\nanalysis recently done by Colli, Gilardi, Krejci and Sprekels as the diffusion\ncoefficient in the equation governing the evolution of the order parameter\ntends to zero. In particular, a well-posedness result is proved for the limit\nsystem. This paper deals with the above limit problem in a less general but\nstill very significant framework and provides a very simple proof of further\nregularity for the solution. As a byproduct, a simple uniqueness proof is given\nas well.\n

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