On a parabolic free boundary problem arising from a Bingham-like flow model with a visco-elastic core |
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Authors: | Angiolo Farina |
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Affiliation: | Università degli Studi di Firenze, Dipartimento di Matematica “U. Dini”, Viale Morgagni 67/a, 50134 Firenze, Italy |
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Abstract: | In this paper we study a two-phase one-dimensional free boundary problem for parabolic equation, arising from a mathematical model for Bingham-like fluids with visco-elastic core presented in [L. Fusi, A. Farina, A mathematical model for Bingham-like fluids with visco-elastic core, Z. Angew. Math. Phys. 55 (2004) 826-847]. 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. Local existence is proved using a fixed point argument based on Schauder's theorem. Uniqueness is proved using a non-standard technique based on a weak formulation of the problem. |
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Keywords: | Bingham fluids Parabolic free boundary problems Schauder theorem |
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