Phase Transitions with Midrange Interactions: A Nonlocal Stefan Model | Zendy

Cristina Brändle | Zendy; Emmanuel Chasseigne | Zendy; Fernando Quirós | Zendy

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Phase Transitions with Midrange Interactions: A Nonlocal Stefan Model

Author(s) -

Cristina Brändle,

Emmanuel Chasseigne,

Fernando Quirós

Publication year - 2012

Publication title -

siam journal on mathematical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.882

H-Index - 92

eISSN - 1095-7154

pISSN - 0036-1410

DOI - 10.1137/110849365

Subject(s) - stefan problem , mathematics , mesoscopic physics , kernel (algebra) , phase transition , mathematical analysis , phase (matter) , scale (ratio) , statistical physics , pure mathematics , physics , boundary (topology) , thermodynamics , condensed matter physics , quantum mechanics

International audienceWe 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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