Geodesic
One-sided Mullins-Sekerka flow does not preserve convexity
Electronic journal of differential equations, Tome 1993 (1993) no. 8
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.
Classification : 35R35, 35J05, 35B50, 53A07
Keywords: Mullins-Sekerka flow, Hele-Shaw flow, Cahn-Hilliard equation, free boundary problem, convexity, curvature 
@article{EJDE_1993__1993_8_a0,
     author = {Mayer,  Uwe F.},
     title = {One-sided {Mullins-Sekerka} flow does not preserve convexity},
     journal = {Electronic journal of differential equations},
     year = {1993},
     volume = {1993},
     number = {8},
     zbl = {0811.35170},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1993__1993_8_a0/}
}
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Mayer,  Uwe F. One-sided Mullins-Sekerka flow does not preserve convexity. Electronic journal of differential equations, Tome 1993 (1993) no. 8. http://geodesic.mathdoc.fr/item/EJDE_1993__1993_8_a0/