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.
|Number of pages||21|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 2001|