Sharp interface limit for the Cahn-Larche system

摘要

We prove rigorously the convergence of the Cahn-Larche 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.