An Allen-Cahn type problem with curvature modification
نویسنده
چکیده
A two component system driven by both interface area and interface curvature is studied with a new phase field model. The Euler-Lagrange equation derived from the free energy functional of the system is a fourth order nonlinear partial differential equation. Formal asymptotic analysis shows that if the curvature impact in the system is strong, there exists a bubble profile in each space dimension. A bubble profile describes a pattern of an inner core of one component surround by an outer membrane of the other component. There are four distinct cases for dimension equal to 1, 2, 3, or 4 and larger. Outlines of the rigorous proofs of the existence theorems are given, based on the formal asymptotic analysis. 2000 AMS subject classification. Primary: 35B25; Secondary: 82B24, 82D60.
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