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One-sided Mullins-Sekerka flow does not preserve convexity. (English) Zbl 0811.35170

Summary: The Mullins-Sekerka model is a nonlocal evolution model for hypersurfaces, which arises as a singular limit for the Cahn-Hilliard equation. Assuming the existence of sufficiently smooth solutions we will show that the one-sided Mullins-Sekerka flow does not preserve convexity.

MSC:

35R35 Free boundary problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35B50 Maximum principles in context of PDEs
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
Full Text: EuDML EMIS