2013/07/04 by Chasseigne, Emmanuel, Sastre-Gomez, Silvia
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1307.1410
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.