Mathematical analysis of a two-phase parabolic free boundary problem derived from a Bingham-type model with visco-elastic core
Bollettino dell'Unione Matematica Italiana (2005)
- Volume: 8-B, Issue: 3, page 781-786
- ISSN: 0392-4041
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topFarina, A., and Fusi, L.. "Mathematical analysis of a two-phase parabolic free boundary problem derived from a Bingham-type model with visco-elastic core." Bollettino dell'Unione Matematica Italiana 8-B.3 (2005): 781-786. <http://eudml.org/doc/195106>.
@article{Farina2005,
abstract = {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.},
author = {Farina, A., Fusi, L.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {781-786},
publisher = {Unione Matematica Italiana},
title = {Mathematical analysis of a two-phase parabolic free boundary problem derived from a Bingham-type model with visco-elastic core},
url = {http://eudml.org/doc/195106},
volume = {8-B},
year = {2005},
}
TY - JOUR
AU - Farina, A.
AU - Fusi, L.
TI - Mathematical analysis of a two-phase parabolic free boundary problem derived from a Bingham-type model with visco-elastic core
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/10//
PB - Unione Matematica Italiana
VL - 8-B
IS - 3
SP - 781
EP - 786
AB - 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.
LA - eng
UR - http://eudml.org/doc/195106
ER -
References
top- DUVAUT, G. - LIONS, J.L., Inequalities in mechanics and physics, Grundlehren der Mathematischen Wissenschaften, Vol. 219, Springer Verlag, 1976. Zbl0331.35002MR521262
- FASANO, A. - PRIMICERIO, M., Classical solutions of general two-phase free boundary problems in one dimension, in Free Boundary Problems: Theory and Applications, Vol. II, A. Fasano, M. Primicerio ed.s, Pitman Research Notes in Mathematics, Vol. 79 (Pitman, 1983), 644-657. Zbl0511.35088MR714939
- FUSI, L. - FARINA, A., On a parabolic free boundary problem arising from a Bingham-like flow model with a visco-elastic core, to appear. Zbl1111.35132
- FUSI, L. - FARINA, A., An Extension of the Bingham model to case of an elastic core, Adv. Math. Sci. Appl., 13 (2003), 113-163. Zbl1038.76003MR2002398
- FUSI, L. - FARINA, A., A mathematical model for Bingham-like fluids with visco-elastic core, ZAMP, 55 (2004), 826-847. Zbl1060.76009MR2087767
- MEIRMANOV, A.M., The Stefan Problem, de Gruyter Expositions in Mahtematics, vol. 3, 1992. Zbl0751.35052MR1154310
- RUBISTEIN, I. - RUBISTEIN, L., Partial Differential Equations in Classical Mathematical Physics, Cambridge University Press, 1998. Zbl0902.35005
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