A center manifold analysis for the Mullins-Sekerka model (Q1381915)

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 \textit{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.