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A nonlocal two-phase Stefan problem

Abstract : We study a nonlocal version of the two-phase Stefan problem, which models a phase transition problem between two distinct phases evolving to distinct heat equations. Mathematically speaking, this consists in deriving a theory for sign-changing solutions of the equation, ut = J ∗ v − v, v = Γ(u), where the monotone graph is given by Γ(s) = sign(s)(|s|−1)+ . We give general results of existence, uniqueness and comparison, in the spirit of [2]. Then we focus on the study of the asymptotic behaviour for sign-changing solutions, which present challenging difficulties due to the non-monotone evolution of each phase.
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https://hal.archives-ouvertes.fr/hal-00841416
Contributor : Emmanuel Chasseigne <>
Submitted on : Thursday, July 4, 2013 - 5:03:27 PM
Last modification on : Thursday, January 9, 2020 - 6:26:03 PM
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  • HAL Id : hal-00841416, version 1
  • ARXIV : 1307.1410

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Emmanuel Chasseigne, Silvia Sastre-Gomez. A nonlocal two-phase Stefan problem. Differential and integral equations, Khayyam Publishing, 2013, 26, pp.1235-1434. ⟨hal-00841416⟩

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