Differential and Integral Equations

A nonlocal two phase Stefan problem

Emmanuel Chasseigne and Silvia Sastre-Gómez

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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, $u_t=J\ast v -v $, $v=\Gamma(u)$, where the monotone graph is given by $\Gamma(s)=\rm{sign}(s)(|s|-1)_+$. We give general results of existence, uniqueness and comparison, in the spirit of [2]. Then we focus on the study of the asymptotic behavior for sign-changing solutions, which present challenging difficulties due to the nonmonotone evolution of each phase.

Article information

Differential Integral Equations, Volume 26, Number 11/12 (2013), 1335-1360.

First available in Project Euclid: 4 September 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 80A22: Stefan problems, phase changes, etc. [See also 74Nxx] 35R09: Integro-partial differential equations [See also 45Kxx] 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 45M05: Asymptotics


Chasseigne, Emmanuel; Sastre-Gómez, Silvia. A nonlocal two phase Stefan problem. Differential Integral Equations 26 (2013), no. 11/12, 1335--1360. https://projecteuclid.org/euclid.die/1378327429

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