Functional Solutions for Fluid Flows Through Porous Media
Cimatti, Giovanni
Bollettino dell'Unione Matematica Italiana, Tome 5 (2012), p. 187-200 / Harvested from Biblioteca Digitale Italiana di Matematica
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The Levy-Caccioppoli global inversion theorem is applied to prove the existence and uniqueness of functional solutions for a problem of flow of a viscous incompressible fluid in a porous medium when the viscosity and the thermal conductivity depend on the temperature. A method based on the Abel integral equation, for determining the dependence of the viscosity from the temperature is also proposed.

Publié le : 2012-02-01
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     author = {Giovanni Cimatti},
     title = {Functional Solutions for Fluid Flows Through Porous Media},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {5},
     year = {2012},
     pages = {187-200},
     zbl = {06078979},
     mrnumber = {2919656},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2012_9_5_1_187_0}
}

Cimatti, Giovanni. Functional Solutions for Fluid Flows Through Porous Media. Bollettino dell'Unione Matematica Italiana, Tome 5 (2012) pp. 187-200. http://gdmltest.u-ga.fr/item/BUMI_2012_9_5_1_187_0/

[1] Abel, N. H., Résolution d'un problém de mécanique, Journal für die reine and angewandte Mathematik, herausgegeben von Crelle, 1, Berlin (1826), 97-101.

[2] Ambrosetti, A. - Prodi, G., Nonlinear Analysis, Cambridge University Press, 1993.

[3] Bear, J., Dynamics of Fluids in Porous Media, Dover Publications, Inc.New York, 1988. | Zbl 1191.76002

[4] Caccioppoli, R., Un principio di inversione per le corrispondenze funzionali, Atti Accad. Naz. Lincei, 16 (1932), 392-400.

[5] Cimatti, G., On the functional solutions of a system of partial differential equations relevant in mathematical physics, Rend. Mat. Univ. Parma, 10 (2010), 423-439. | MR 2789450 | Zbl 1216.35022

[6] Cimatti, G., Application of the Abel integral equation to an inverse problem in thermoelectricity, Eur. Jour. Appl. Math (to appear). | MR 2558705 | Zbl 1180.80013

[7] Gorenflo, R. - Vessella, S., Abel Integral Equations, Springer-Verlag, Berlin, 1980. | MR 1095269

[8] Levy, P., Sur les functions de lignes implicites, Bull. Soc. Mat. Fr., 48, 13-27. | MR 1504790 | Zbl 47.0381.01

[9] Nield, D. A. - Bejan, A., Convection in Porous Media, Springer Verlag, Berlin, 1998. | MR 1656781 | Zbl 1268.76001

[10] Protter, M. - Weinberger, H., Maximus Principle in Differential Equations, Springer-Verlag, New York, 1963. | MR 762825

[11] Tonelli, L., Su un problema di Abel, Math. Ann.99 (1928), 183-199. | MR 1512447

[12] Tricomi, F. G., Integral Equations, Interscience Publishers, London1957. | MR 94665