Mayer, Uwe F. One-sided Mullins-Sekerka flow does not preserve convexity. (English) Zbl 0811.35170 Electron. J. Differ. Equ. 1993, No. 08, 7 p. (1993). 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. Cited in 2 Documents 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 Keywords:Hele-Shaw flow; Cahn-Hilliard equation; free boundary problem; curvature; Mullins-Sekerka model; convexity PDFBibTeX XML Full Text: EuDML EMIS