Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 33, Issue 12, Pages 2225-2256Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605300802553906
Keywords
Free boundary problems; Interacting particle systems; Stefan equation
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Funding
- NSF [DMS-07-00732, DMS-03-06167 (]
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We study a novel two-sided Stefan problemmotivated by the study of certain 2D interfacesin which boundaries at both sides of the sample encroach into the bulk with rate equal to the boundary value of the gradient. Here the density is in [0, 1] and takes the two extreme values at the two free boundaries. It is noted that the problem is borderline ill-posed: densities in excess of unity liable to cause catastrophic behavior. We provide a general proof of existence and uniqueness for these systems under the condition that the initial data is in [0, 1] and with some mild conditions near the boundaries. Applications to 2D shapes are provided, in particular motion by weighted mean curvature for the relevant interfaces is established.
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