2021/11/30 by Ioannis Athanasopoulos, Luis Caffarelli, Athanasopoulos, Ioannis +3
Computer Science · Engineering · #35R09 #35R11 #45K05 #80A22 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in engineering #Phase Change Materials Research
paper · pdf · doi:10.48550/arxiv.2111.15600
openalex publication_date 2021/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The non-local in space two-phase Stefan problem (a prototype in phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admits a unique weak solution. This formulation makes Stefan problem to be part of the General Filtration Problems; a class which includes the Porous Medium Equation. In this work, we prove that the weak solutions to both Stefan and Porous Media problems are continuous.