Processi di filtrazione in un mezzo poroso con interazioni fra il liquido e la matrice porosa
Talamucci, F.
Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001), p. 365-380 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

A model of filtration in a multispecies porous medium accompanied by a strong interaction between the flow and the porous matrix is presented. The species removed by the flow are both fine particles and other substances which diffuse in the liquid. The accumulation of the migrating particles in proximity of the outflow surface gives rise to the formation of a compact layer with high hydraulic resistance. The corresponding mathematical model consists in a set of partial differential equations of hyperbolic and parabolic type. to be solved in a free domain: the free boundary is the surface separating the compact layer from the rest of the medium. Under specific assumptions, which are expressive from the physical point of view, a result of existence (globally in time) and uniqueness of the solution can be proved, by means of fixed point techniques. Finally, some qualitative aspects of the solution are examined.

Publié le : 2001-06-01
@article{BUMI_2001_8_4B_2_365_0,
     author = {F. Talamucci},
     title = {Processi di filtrazione in un mezzo poroso con interazioni fra il liquido e la matrice porosa},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4-A},
     year = {2001},
     pages = {365-380},
     zbl = {1177.76418},
     mrnumber = {1831994},
     language = {it},
     url = {http://dml.mathdoc.fr/item/BUMI_2001_8_4B_2_365_0}
}

Talamucci, F. Processi di filtrazione in un mezzo poroso con interazioni fra il liquido e la matrice porosa. Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001) pp. 365-380. http://gdmltest.u-ga.fr/item/BUMI_2001_8_4B_2_365_0/

[1] Fasano, A., Some nonstandard one-dimensional filtration problems, The Bulletin of the Faculty of Education, Chiba University, 44, 1996 | Zbl 0873.76082

[2] Fasano, A.-Primicerio, M., Mathematical models for filtration through porous media interacting with the flow, in Nonlinear Mathematical problems in Industry, I, M. Kawarada, N. Kenmochi, N. Yanagihara eds., Math. Sci. & Appl., 1, pp. 61-85, Gakkotosho, Tokyo. | Zbl 0875.35149

[3] Fasano, A.-Primicerio, M., Flows through saturated mass exchanging porous media under high pressure gradients, Proc. of Calculus of Variations, Applications and Computations, C. Bandle et al. eds. - Pitman Res. Notes Math. Series 326, 1994. | MR 1419338 | Zbl 0839.76083

[4] Fasano, A.-Talamucci, F., A comprehensive mathematical model for a multi-species flow through ground coffee, SIAM J. Math. Anal. Vol. 31, No. 2 (1999), 251-273. | MR 1740938 | Zbl 0937.35187

[5] Ladyženskaja, O. A.-Solonnikov, V. A.-Ural'Ceva, N. N., Linear and quasilinear equations of parabolic type, Transl. of Math. Monographs, vol. 23, American Mathematical Society. | MR 241822 | Zbl 0174.15403

[6] Petracco, M., Espresso coffee brewing dynamics: development of mathematical and computational models, 15éme Colloque Scient. Internat. sur le Café, Associat. Scientif. Internat. du Café, Paris (1993).

[7] Talamucci, F., Analysis of coupled heat-mass transport in freezing saturated soils, Surveys on Mathematics for Industry, vol. 7, Springer-Verlag (1997), pp. 93-139. | MR 1612779 | Zbl 0901.76084

[8] Talamucci, F., Flow through a porous medium with mass removal and diffusion, Nonlinear Differential Equations and Applications, 5 (1998), 427-444. | MR 1662066 | Zbl 0922.35137