Geodesic
Continuity of the temperature in a multi-phase transition problem. Part II
Ugo Gianazza1 orcid ; Naian Liao2 orcid
1Università di Pavia, Pavia, Italy
2Universität Salzburg, Salzburg, Austria
Interfaces and free boundaries, Tome 26 (2024) no. 4, pp. 625-674

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DOI

Local continuity is established for locally bounded, weak solutions to a doubly non-linear parabolic equation that models the temperature of a material undergoing a multi-phase transition. The enthalpy, as a maximal monotone graph of the temperature, is allowed to possess several jumps and/or infinite derivatives at the transition temperatures. The effect of the p-Laplacian-type diffusion is also considered. As an application, we demonstrate a continuity result for the saturation in the flow of two immiscible fluids through a porous medium, when irreducible saturation is present.
DOI : 10.4171/ifb/522
Classification : 35K65, 35K92, 35B65, 76S05, 80A22
Mots-clés : phase transition, parabolic p-Laplacian, modulus of continuity, two-phase flow

Ugo Gianazza  1   ; Naian Liao  2

1 Università di Pavia, Pavia, Italy
2 Universität Salzburg, Salzburg, Austria 
Ugo Gianazza; Naian Liao. Continuity of the temperature in a multi-phase transition problem. Part II. Interfaces and free boundaries, Tome 26 (2024) no. 4, pp. 625-674. doi: 10.4171/ifb/522
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     title = {Continuity of the temperature in a multi-phase transition problem. {Part~II}},
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     year = {2024},
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     number = {4},
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