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A continuous dependence result for a nonstandard system of phase field equations

Please always quote using this URN:urn:nbn:de:0296-matheon-12230
  • The present note deals with a nonstandard systems of differential equations describing a two-species phase segregation. This system naturally arises in the asymptotic analysis carried out recently by the same authors, as the diffusion coefficient in the equation governing the evolution of the order parameter tends to zero. In particular, an existence result has been proved for the limit system in a very general framework. On the contrary, uniqueness was shown by assuming a constant mobility coefficient. Here, we generalize this result and prove a continuous dependence property in the case that the mobility coefficient suitably depends on the chemical potential.

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Metadaten
Author:Pierluigi Colli, Gianni Gilardi, Pavel Krejcí, Jürgen Sprekels
URN:urn:nbn:de:0296-matheon-12230
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2013/05/29
Release Date:2013/05/29
Tag:continuous dependence; nonlinear differential equations; nonstandard phase field system; uniqueness
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B30 Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equations
Preprint Number:1018
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