Abstract
A free boundary problem due to Nishiura and Ohnishi is solved in one space dimension. That problem was derived, during their study of phase separation phenomena in diblock copolymers, as an asymptotic limit of pattern-forming PDEs generalizing that of Cahn and Hilliard. The free boundary problem in one dimension reduces to a linear system of ODEs for the lengths of the intervals between interfaces. This system also arises in a completely different context as the spatial discretization of a simple heat equation in a medium with periodic properties. (The medium is homogeneous in an important special case.) The initial-value problem for this system is completely solved, and global stability results for stationary solutions (in which the interfaces are regularly spaced) are obtained. Nucleation phenomena are briefly discussed.
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