Abstract:In this paper, we develop the theory for the two-phase Stefan problem with finite energy, possibly non-empty mushy region, and space-dependent melting temperature. Specifically, we prove the existence of weak solutions with an elliptic regularization scheme. Our existence theorem provides information about the regularity of the solutions: we prove that the temperature of weak solutions is in $H^1$ for all times, that the enthalpy is well defined and bounded for all times, and that both the enthalpy and the temperature are weakly continuous in time. Finally, we establish a comparison principle for weak solutions on general unbounded domains and use it to show that every weak solution is recovered by the approximation scheme.
From: Filippo Paiano [view email]
[v1]
Sat, 30 May 2026 20:41:29 UTC (52 KB)
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