Advances in Differential Equations

Global solutions to a generalized Cahn-Hilliard equation with viscosity

Elena Bonetti, Wolfgang Dreyer, and Giulio Schimperna

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We address a viscous Cahn-Hilliard equation describing the phase separation process in a binary alloy. Such a material is subject to the influence of internal and external mechanical stresses, whose contribution is assumed to be known. The physical modelling refers to a recent work by Dreyer and Müller. The main features and difficulties of this model are given by a highly nonlinear fourth order elliptic term, a strong constraint imposed by the presence of a double obstacle energy potential, and the dependence of the mobility matrix on the concentration variable (i.e., the unknown of the problem). We are able to prove global existence of solutions of the corresponding initial boundary value problem by using approximation and compactness tools. Hence, we perform some asymptotic analysis of the problem and obtain, at the limit, two models of independent physical interest.

Article information

Source
Adv. Differential Equations Volume 8, Number 2 (2003), 231-256.

Dates
First available in Project Euclid: 19 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355926863

Mathematical Reviews number (MathSciNet)
MR1948045

Zentralblatt MATH identifier
1032.35075

Subjects
Primary: 35K35: Initial-boundary value problems for higher-order parabolic equations
Secondary: 35R35: Free boundary problems 74N25: Transformations involving diffusion 82B26: Phase transitions (general)

Citation

Bonetti, Elena; Dreyer, Wolfgang; Schimperna, Giulio. Global solutions to a generalized Cahn-Hilliard equation with viscosity. Adv. Differential Equations 8 (2003), no. 2, 231--256. https://projecteuclid.org/euclid.ade/1355926863.


Export citation