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A stochastic selection principle in case of fattening for curvature flow


Reference:

Dirr, N., Luckhaus, S. and Novaga, M., 2001. A stochastic selection principle in case of fattening for curvature flow. Calculus of Variations and Partial Differential Equations, 13 (4), pp. 405-425.

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Abstract

Consider two disjoint circles moving by mean curvature plus a forcing term which makes them touch with zero velocity. It is known that the generalized solution in the viscosity sense ceases to be a curve after the touching (the so-called fattening phenomenon). We show that after adding a small stochastic forcing epsilondW, in the limit epsilon --> 0 the measure selects two evolving curves, the upper and lower barrier in the sense of De Giorgi. Further we show partial results for nonzero epsilon.

Details

Item Type Articles
CreatorsDirr, N., Luckhaus, S. and Novaga, M.
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code7471
Additional InformationID number: ISI:000173196000001

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