Abstract
Eguchi--Oki--Matsumura equations are introduced to describe the dynamics of pattern formation that arises from phase separation in some binary alloys. The model extends the well-known Cahn--Hilliard equation and consists of coupled two functions; one is the local concentration and the other is the local degree of order. We show the existence of a solution, its asymptotic profile, and in part the structure of steady state solutions. Computational studies are also given.
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