Loss of convexity for a modified Mullins-Sekerka model arising in diblock copolymer melts

Joachim Escher and Uwe F. Mayer

Abstract: This modified (two-sided) Mullins-Sekerka model is a nonlocal evolution model for closed hypersurfaces, which appears as a singular limit of a modified Cahn-Hilliard equation describing microphase separation of diblock copolymer. Under this evolution the propagating interfaces maintain the enclosed volumes of the two phases. We will show by means of an example that this model does not preserve convexity in two space dimensions.

Key words:Mullins-Sekerka flow, Cahn-Hilliard equation, maximum principle, Poisson integral formula, free boundary problem, harmonic functions, curvature.

You can download a copy of this article (about 11 pages plus references).

Mayer11.ps.gz This file is in gzipped postscript format. (92 Kbytes)

Mayer11.pdf This file is in Portable Document Format. (255 Kbytes)

Back