A center manifold analysis for the Mullins-Sekerka model. (English) Zbl 0896.35142
The authors consider the Mullins-Sekerka model which is a volume preserving and area shrinking generalization of the mean curvature flow. Using center manifold theory they prove a higher-dimensional analogue of a result of X. Chen [Arch. Ration. Mech. Anal. 123, 117-151 (1993; Zbl 0780.35117)] for two dimensions. They show that if the initial hypersurface \(\Gamma_0\) is close to a sphere, then \(\Gamma_t\) exists for all \(t>0\) and converges exponentially fast to a sphere.
Reviewer: B.Priwitzer (Tübingen)
MSC:
| 35R35 | Free boundary problems for PDEs |
| 35K55 | Nonlinear parabolic equations |
| 34C30 | Manifolds of solutions of ODE (MSC2000) |
Keywords:
mean curvature flowCitations:
Zbl 0780.35117References:
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