Sharp interface limit for the Cahn–Larché system

Article type: Research Article

Authors: Abels, Helmut^; | Schaubeck, Stefan

Affiliations: Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany

Note: [] Corresponding author. E-mail: helmut.abels@mathematik.uni-regensburg.de

Abstract: We prove rigorously the convergence of the Cahn–Larché system, which is a Cahn–Hilliard system coupled with the system of linearized elasticity, to a modified Hele–Shaw problem as long as a classical solution of the latter system exists. By matched asymptotic expansion we construct approximate solutions and estimate the difference between the true and the approximate solutions.

Keywords: sharp interface limit, diffuse interface model, Cahn–Hilliard equation, linearized elasticity, Hele–Shaw system, matched asymptotic expansion

DOI: 10.3233/ASY-141268

Journal: Asymptotic Analysis, vol. 91, no. 3-4, pp. 283-340, 2015