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A nonlocal one-phase Stefan problem that develops mushy regions

Abstract : We study a nonlocal version of the one-phase Stefan problem which develops mushy regions, even if they were not present initially, a model which can be of interest at the mesoscopic scale. The equation involves a convolution with a compactly supported kernel. The created mushy regions have the size of the support of this kernel. If the kernel is suitably rescaled, such regions disappear and the solution converges to the solution of the usual local version of the one-phase Stefan problem. We prove that the model is well posed, and give several qualitative properties. In particular, the long-time behavior is identified by means of a nonlocal mesa solving an obstacle problem.
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https://hal.archives-ouvertes.fr/hal-00626418
Contributor : Emmanuel Chasseigne <>
Submitted on : Monday, September 26, 2011 - 10:58:58 AM
Last modification on : Friday, April 19, 2019 - 1:30:08 PM
Document(s) archivé(s) le : Tuesday, December 27, 2011 - 2:22:03 AM

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Cristina Brändle, Emmanuel Chasseigne, Fernando Quirós. A nonlocal one-phase Stefan problem that develops mushy regions. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2012, 44 (4), pp.3071-3100. ⟨10.1137/110849365⟩. ⟨hal-00626418⟩

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