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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 315768, 7 pages
http://dx.doi.org/10.1155/2014/315768
Research Article

Mean Curvature Type Flow with Perpendicular Neumann Boundary Condition inside a Convex Cone

School of Mathematics and Statistics, Hubei University, Wuhan 430062, China

Received 9 January 2014; Accepted 30 June 2014; Published 17 July 2014

Academic Editor: Narcisa C. Apreutesei

Copyright © 2014 Fangcheng Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the evolution of hypersurfaces with perpendicular Neumann boundary condition under mean curvature type flow, where the boundary manifold is a convex cone. We find that the volume enclosed by the cone and the evolving hypersurface is invariant. By maximal principle, we prove that the solutions of this flow exist for all time and converge to some part of a sphere exponentially as tends to infinity.