PreprintarXiv licencearXiv
Existence of weak solutions to two-phase Stefan problems for parabolic partial differential equation system
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 W1,2-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.
Related
- On the Existence, Uniqueness, and Numerical Solutions of a Time-Fractional Pseudo-Parabolic Equation Under Periodic Boundary Conditions
- Nonnegative Viscosity and Weak Solutions to Trudinger's Parabolic Equation
- Existence of multi-peak solutions for singularly perturbed problems in the zero-mass case
- Existence and Nonexistence of Solutions of Certain type of Nonlinear Differential and Differential-Difference Equations
- Lyapunov-Krasovsky Functionals and the Existence of Unbounded Solutions of Functional-Differential Equations of Retarded Type
BibTeX
@misc{kakiuchi2026existence,
title = {{Existence of weak solutions to two-phase Stefan problems for parabolic partial differential equation system}},
author = {Hana Kakiuchi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27401},
eprint = {2609.27401},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27401},
}
RIS
TY - UNPB
TI - Existence of weak solutions to two-phase Stefan problems for parabolic partial differential equation system
AU - Hana Kakiuchi
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27401
UR - https://arxiv.org/abs/2609.27401
AB - 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.
ER -