Constructs global-time weak solutions to the nonlocal Stefan problem via martingale transport, establishes connection to parabolic obstacle problem, and proves exponential convergence for the melting case.
Kim,The supercooled stefan problem in one dimension, Communications on Pure and Applied Analysis (CPAA)11 (2012), no
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The Nonlocal Stefan Problem via a Martingale Transport
Constructs global-time weak solutions to the nonlocal Stefan problem via martingale transport, establishes connection to parabolic obstacle problem, and proves exponential convergence for the melting case.