On a Homogenization Effect for a Two-Dimensional Diffusion Plus Transport Equation

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1. CONSTANTIN, P. - KISELEV, A. - RYZHIK, L. - ZLATOŠ, A., Diffusion and mixing in fluid flow, Ann. of Math. (2), 168, no. 2 (2008), 643-674. Zbl1180.35084MR2434887DOI10.4007/annals.2008.168.643
2. 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. Zbl1387.35493MR2733257DOI10.1137/090776895
3. 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. MR1493039
4. 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. Zbl0153.42103MR225015
5. SPAGNOLO, S., Sulla convergenza di soluzioni di equazioni paraboliche ed ellitiche, Ann. Scuola Norm. Sup. Pisa (3) 22 (1968), 571-597. MR240443
6. 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 (BirkhäuserBoston, MA, 1997). MR1493037
7. 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 (BirkhäuserBoston, MA, 1997). MR540123
8. 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). MR909716
9. 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. Zbl0774.35008MR1069518DOI10.1017/S0308210500020606
10. 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). Zbl0803.46039MR1260449
11. 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. Zbl0894.49002MR1474002
12. 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). MR1804685DOI10.1007/BFb0106742
13. TARTAR, L., Qu'est-ce que l'homogénéisation?, Portugaliae Mathematica, Vol. 64, Fasc. 4 (2007), 389-444. Zbl1145.35003MR2374397DOI10.4171/PM/1791
14. 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. MR2582099DOI10.1007/978-3-642-05195-1
15. YOUNG, L., Lectures on the calculus of variations and optimal control theory, W. B. Saunders Co., Philadelphia-London-Toronto, Ont. (1969), xi+331. Zbl0177.37801MR259704