Geodesic
Mathematical analysis of a two-phase parabolic free boundary problem derived from a Bingham-type model with visco-elastic core
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 781-786

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this paper we consider a two-phase one-dimensional free boundary problem for the heat equation, arising from a mathematical model for a Bingham-like fluid with a visco-elastic core. The main feature of this problem consists in the very peculiar structure of the free boundary condition, not allowing to use classical tools to prove well posedness. Existence of classical solution is proved using a fixed point argument based on Schauder's theorem. Uniqueness is proved using a technique based on a weak formulation of the problem. 
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     author = {Farina, A. and Fusi, L.},
     title = {Mathematical analysis of a two-phase parabolic free boundary problem derived from a {Bingham-type} model with visco-elastic core},
     journal = {Bollettino della Unione matematica italiana},
     pages = {781--786},
     publisher = {mathdoc},
     volume = {Ser. 8, 8B},
     number = {3},
     year = {2005},
     zbl = {1178.35222},
     mrnumber = {MR2182430},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a16/}
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Farina, A.; Fusi, L. Mathematical analysis of a two-phase parabolic free boundary problem derived from a Bingham-type model with visco-elastic core. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 781-786. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a16/