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.
Author: | Pierluigi Colli, Gianni Gilardi, Pavel Krejcí, Jürgen Sprekels |
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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 |