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arXiv · 2609.27401

Existence of weak solutions to two-phase Stefan problems for parabolic partial differential equation system

Hana Kakiuchi
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Abstract

In our previous results, we have proposed a new free boundary problem representing the bread baking process in a hot oven. The problem consists of conservation laws for the internal energy and water mass, the Stefan condition, the boundary and initial conditions. We note that the boundary condition for the water content contains the temperature at the boundary. Accordingly, we do not expect a strong solution for $W^{1,2}$-initial data. To address this difficulty, we established strong solvability by assuming stricter conditions for the initial functions in [3]. In contrast, this paper aims to prove the existence of a weak solution, when these assumptions for initial functions are relaxed.

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Hana Kakiuchi. 2026-09-23. Existence of weak solutions to two-phase Stefan problems for parabolic partial differential equation system. https://arxiv.org/abs/2609.27401

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