Sharp interface limit for the Cahn–Larché system

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.