WIAS Preprint No. 1778, (2013)

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


Authors

  • Colli, Pierluigi
    ORCID: 0000-0002-7921-5041
  • Gilardi, Gianni
    ORCID: 0000-0002-0651-4307
  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2010 Mathematics Subject Classification

  • 35K61 35A05 35B30

Keywords

  • nonstandard phase field system, nonlinear differential equations, uniqueness, continuous dependence

DOI

10.20347/WIAS.PREPRINT.1778

Abstract

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.

Appeared in

  • Math. Methods Appl. Sci., 37 (2014) pp. 1318--1324.

Download Documents