Si considera l'insorgere della convezione naturale in un mezzo poroso (Horton-Rogers-Lapwood problem), assumendo che la viscosità del fluido dipenda dalla temperatura. Adoperando il metodo diretto di Liapunov, si effettua l'analisi della stabilitá non lineare della soluzione di conduzione per i modelli di Darcy e di Forchheimer.
@article{BUMI_2001_8_4B_1_143_0, author = {F. Capone}, title = {On the onset of convection in porous media: temperature depending viscosity}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {4-A}, year = {2001}, pages = {143-156}, zbl = {1177.76402}, mrnumber = {1821403}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2001_8_4B_1_143_0} }
Capone, F. On the onset of convection in porous media: temperature depending viscosity. Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001) pp. 143-156. http://gdmltest.u-ga.fr/item/BUMI_2001_8_4B_1_143_0/
[1] | Zbl 0769.76001
- - : Theory of fluid flows through natural rocks, Kluwer Academic Publishers (1990).[2] Nonlinear stability analysis of convection for fluids with exponentially temperature-dependent viscosity, Acta Mechanica, 107 (1994), 53. | MR 1299152 | Zbl 0846.76033
- ,[3] Nonlinear stability analysis of the Bénard problem for fluids with a convex nonincreasing temperature depending viscosity, Continuum Mech. Thermodyn., 7 (1995), 297-309. | MR 1349424 | Zbl 0830.76034
- ,[4] On the influence of the Forchheimer term in convective instabilities in porous media for fluids with temperature depending viscosity, Rend. Circolo Mat. Palermo, Serie II, Suppl. 57 (1998), 91-95. | MR 1708498 | Zbl 0962.76524
- ,[5] Temperature dependent viscosity and its influence on the onset of convetion in a porous medium, Rend. Acc. Sc. fis. mat. Napoli, vol. LXVI (1999), 159-172. | MR 1771535 | Zbl 0972.76033
- ,[6] | MR 128226 | Zbl 0142.44103
, Hydrodynamic and hydromagnetic stability, New York, Dover (1961).[7] | MR 1396085 | Zbl 0862.35001
- , Qualitative estimates for partial differential equations. An introduction, Boca Raton, Florida: CRC Press (1996).[8] Nonlinear equation governing flow in a saturated porous medium, Water Resources Res., 18, 1049-1052 and 19 (1982), 591.
- - ,[9] Stability of fluid motions I-II, Springer Tracts in Natural Philosophy, vols. 27-28 (1976). | MR 449147 | Zbl 0345.76022
,[10] | MR 1656781 | Zbl 0924.76001
- , Convection in porous media, Berlin Heidelberg New York: Springer-Verlag (1992).[11] Nonlinear convective stability in a porous medium, Studies In Appl. Math. (1996), 273-288. | MR 1378863 | Zbl 0853.76025
- ,[12] Metodi variazionali per la stabilità asintotica in media in magnetoidrodinamica, Ann. Mat. Pura Appl., 78 (1968), 339-364. | MR 229424 | Zbl 0182.29402
, , The energy method, stability and nonlinear convection, Berlin Heidelberg New York Tokyo: Springer (1992).