Continuous dependence for a nonstandard Cahn-Hilliard system with nonlinear atom mobility
Please always quote using this URN:urn:nbn:de:0296-matheon-12253
- 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 [22]; 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 [12].
Author: | Pierluigi Colli, Gianni Gilardi, Paolo Podio-Guidugli, Jürgen Sprekels |
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URN: | urn:nbn:de:0296-matheon-12253 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2015/12/23 |
Release Date: | 2015/12/23 |
Tag: | existence of solutions; new uniqueness proof; nonlinear system of partial differential equations; phase-field model |
Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
MSC-Classification: | 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 |
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Axx Generalities, axiomatics, foundations of continuum mechanics of solids / 74A15 Thermodynamics | |
Preprint Number: | 1086 |