On a Homogenization Effect for a Two-Dimensional Diffusion Plus Transport Equation
Tartar, Luc
Bollettino dell'Unione Matematica Italiana, Tome 5 (2012), p. 281-307 / Harvested from Biblioteca Digitale Italiana di Matematica
Publié le : 2012-06-01
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     author = {Luc Tartar},
     title = {On a Homogenization Effect for a Two-Dimensional Diffusion Plus Transport Equation},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {5},
     year = {2012},
     pages = {281-307},
     zbl = {1291.35238},
     mrnumber = {2977250},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2012_9_5_2_281_0}
}
Tartar, Luc. On a Homogenization Effect for a Two-Dimensional Diffusion Plus Transport Equation. Bollettino dell'Unione Matematica Italiana, Tome 5 (2012) pp. 281-307. http://gdmltest.u-ga.fr/item/BUMI_2012_9_5_2_281_0/

[CKRZ] Constantin, P. - Kiselev, A. - Ryzhik, L. - Zlatoš, A., Diffusion and mixing in fluid flow, Ann. of Math. (2), 168, no. 2 (2008), 643-674. | MR 2434887 | Zbl 1180.35084

[INRZ] Iyer, G. - Novikov, A. - Ryzhik, L. - Zlatoš, A., Exit times of diffusions with incompressible drift, SIAM J. Math. Anal., 42, no. 6 (2010), 2484-2498. | MR 2733257 | Zbl 1387.35493

[Mu] Murat, F., H-convergence, Séminaire d'analyse fonctionnelle et numérique, Université d'Alger, 1977-78. English translation: Murat, F. - Tartar, L., H-convergence, Topics in the mathematical modelling of composite materials, 21-43, Progr. Nonlinear Differential Equations Appl., 31, Birkhäuser, Boston, MA, 1997. | MR 1493039

[Sp1] Spagnolo, S., Sul limite delle soluzioni di problemi di Cauchy relativi all'equazione del calore, Ann. Scuola Norm. Sup. Pisa, (3) 21 (1967), 657-699. | MR 225015 | Zbl 0153.42103

[Sp2] Spagnolo, S., Sulla convergenza di soluzioni di equazioni paraboliche ed ellitiche, Ann. Scuola Norm. Sup. Pisa (3) 22 (1968), 571-597. | MR 240443

[Ta74] Tartar, L., Problèmes de contrôle des coefficients dans des équations aux dérivées partielles, Control theory, numerical methods and computer systems modelling (Internat. Sympos., IRIA LABORIA, Rocquencourt, 1974), pp. 420-426. Lecture Notes in Econom. and Math. Systems, Vol. 107, Springer, Berlin, 1975. English translation: F. Murat - L. Tartar, On the control of coefficients in partial differential equations, Topics in the mathematical modelling of composite materials, 1-8, Prog. Nonlinear Differential Equations Appl., 31 (Birkhäuser Boston, MA, 1997). | MR 1493037

[Ta77] Tartar, L., Estimations de coefficients homogénéisés, Computing methods in applied sciences and engineering (Proc. Third Internat. Sympos., Versailles, 1977), I, pp. 364-373, Lecture Notes in Math., 704, (Springer, Berlin, 1979). English translation: Estimations of homogenized coefficients, Topics in the mathematical modelling of composite materials, 9-20, Prog. Nonlinear Differential Equations Appl., 31 (Birkhäuser Boston, MA, 1997). | MR 540123

[Ta83] Tartar, L., Estimations fines des coefficients homogénéisés, Ennio De Giorgi colloquium (Paris, 1983), 168-187, Res. Notes in Math., 125 (Pitman, Boston, MA-London, 1985). | MR 909716

[Ta90] Tartar, L., H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A, 115, no. 3-4 (1990), 193-230. | MR 1069518 | Zbl 0774.35008

[Ta93] Tartar, L., Remarks on Some Interpolation Spaces, in Boundary value problems for partial differential equations and applications, 229-252, RMA Res. Notes Appl. Math., 29 (Masson, Paris, 1993). | MR 1260449 | Zbl 0803.46039

[Ta95] Tartar, L., Remarks on the Homogenization Method in Optimal Design Problems, in Homogenization and Applications to Material Sciences, Proc. Nice 1995, D. Cioranescu, A. Damlamian and P. Donato Editors, Gakuto Int. Series, Math. Sciences and Applications vol. 9, Gakkokotosho, Tokyo, Japan (1997) 393-412. | MR 1474002 | Zbl 0894.49002

[Ta98] Tartar, L., An Introduction to the Homogenization Method in Optimal Design, Optimal Shape Design, Tróia, 1998, 47-156, Lecture Notes in Math., Vol. 1740 (Springer, Berlin, 2000). | MR 1804685

[Ta07] Tartar, L., Qu'est-ce que l'homogénéisation?, Portugaliae Mathematica, Vol. 64, Fasc. 4 (2007), 389-444. | MR 2374397 | Zbl 1145.35003

[Ta09] Tartar, L., The General Theory of Homogenization: A Personalized Introduction, Lecture Notes of the Unione Matematica Italiana, 7. Springer-Verlag, Berlin; UMI (Bologna, 2009), xxii+470. | MR 2582099

[Yo] Young, L., Lectures on the calculus of variations and optimal control theory, W. B. Saunders Co., Philadelphia-London-Toronto, Ont. (1969), xi+331. | MR 259704 | Zbl 0177.37801