WIAS Preprint No. 1742, (2012)

Continuous dependence for a nonstandard Cahn--Hilliard system with nonlinear atom mobility



Authors

  • Colli, Pierluigi
  • Gilardi, Gianni
  • Podio-Guidugli, Paolo
  • Sprekels, Jürgen

2010 Mathematics Subject Classification

  • 35K61 35A05 74A15

Keywords

  • phase-field model, nonlinear system of partial differential equations, existence of solutions, new uniqueness proof

Abstract

This note is concerned with a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions. The system arises from a model of two-species phase segregation on an atomic lattice [Podio-Guidugli 2006]; it consists of the balance equations of microforces and microenergy; the two unknowns are the order parameter $rho$ and the chemical potential $mu$. Some recent results obtained for this class of problems is reviewed and, in the case of a nonconstant and nonlinear atom mobility, uniqueness and continuous dependence on the initial data are shown with the help of a new line of argumentation developed in Colli/Gilardi/Podio-Guidugli/Sprekels 2012.

Appeared in

  • Rend. Semin. Mat. Univ. Politec. Torino, 70 (2012) pp. 27--52.

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