Kinetic decomposition for periodic homogenization problems

SIAM Journal on Mathematical Analysis

Volumn 41, Issue 1, 2009, Pages 360-390

  Jabin, Pierre Emmanuel ^a   Tzavaras, Athanasios E ^b  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

^b University of Maryland   (United States)

Author keywords

Homogenization; Hyperbolic problems; Kinetic formulation; Transport equations

Indexed keywords

ANALYTICAL TOOL; ASYMPTOTIC EXPANSION; EFFECTIVE EQUATIONS; ENHANCED DIFFUSION; HOMOGENIZATION; HOMOGENIZATION PROBLEMS; HYPERBOLIC PROBLEMS; KINETIC EQUATIONS; LIMIT PROBLEM; MULTISCALES; NEW RESULTS; OSCILLATORY FUNCTIONS; PERIODIC HOMOGENIZATION; TRANSPORT EQUATION;

ASYMPTOTIC ANALYSIS; COMPUTATIONAL MECHANICS; INTEGRAL EQUATIONS; KINETIC ENERGY; KINETIC THEORY; KINETICS;

DECOMPOSITION;

EID: 70450271071     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/080735837     Document Type: Article

References (23)

1. G. ALLAIRE, Homogenization and two-scale convergence, SIAM J. Math. Anal., 23 (1992), pp. 1482-1518
2. G. ALLAIRE AND M. VANNINATHAN, Homogenization of the Schrödinger equation with a time oscillating potential, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1-16
3. Y. AMIRAT, K. HAMDACHE, AND A. ZIANI, Homogénéisation d'équations hyperboliques du premier ordre et application aux écoulements miscibles en milieu poreux, Ann. Inst. H. Poincaré Anal. Non Linéaire, 6 (1989), pp. 397-417 (i n French)
4. T. ARBOGAST, J. DOUGLAS, JR., AND U. HORNUNG, Derivation of the double porosity model of single phase flow via homogenization theory, SIAM J. Math. Anal., 21 (1990), pp. 823-836
5. M. AVELLANEDA AND A.J. MAJDA, An integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows, Comm. Math. Phys., 138 (1991), pp. 339-391
6. A. BENSOUSSAN, J.L. LIONS, AND G. PAPANICOLAOU, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978
7. Y. BRENIER, Remarks on some linear hyperbolic equations with oscillatory coefficients,in Proceedings of the Third International Conference on Hyperbolic Problems, Vols. I and II (Uppsala, 1990), Studentlitteratur, Lund, Sweden, 1991, pp. 119-130
8. Y. CAPDEBOSCQ, Homogenization of a spectral problem with drift, Proc. Roy. Soc. Edinburgh Sect. A, 132 (2002), pp. 567-594
9. Y. CAPDEBOSCQ, Homogénéisation des Modèles de Diffusion en Neutronique,Ph.D. thesis. These Université Paris 6, Paris, 1999
10. J. CASADO-DÍAZ, M. LUNA-LAYNEZ, AND J.D. MARTÍN, An adaptation of the multi-scale methods for the analysis of very thin reticulated structures, C. R.Acad. Sci. ParisSer.I, 332 (2001), pp. 223-228
11. W. E, Homogenization of linear and nonlinear transport equations, Comm. Pure Appl. Math., 45 (1992), pp. 301-326
12. A. FANNJIANG AND G. PAPANICOLAOU, Convection enhanced diffusion for periodic flows,SIAM J. Appl. Math., 54 (1994), pp. 333-408
13. P. GÉRARD, P.A. MARKOWICH, N.J. MAUSER, AND F. POUPAUD, Homogenization limits and Wigner transforms, Comm. Pure Appl. Math., 50 (1997), pp. 323-379 (Pubitemid 127383077)
14. T. GOUDON AND F. POUPAUD, Homogenization of transport equations: Weak mean field approximation, SIAM J. Math. Anal., 36 (2005), pp. 856-881
15. K. HAMDACHE, Homogénéisation non locale d'équations hyperboliques, in Nonlinear Partial Differential Equations and Their Applications, Collège deFranceSeminar, Vol.XII, Pitman Res. Notes Math. 302, Longman Sci. Tech., Harlow, 1 994, pp. 97-112
16. L. HORMANDER, The Analysis of Linear Partial Differential Operators, Springer, New York, 1990
17. T.Y. HOU AND X. XIN, Homogenization of linear transport equations with oscillatory vector fields, SIAM J. Appl. Math., 52 (1992), pp. 34-45
18. D.W. MCLAUGHLIN, G.C. PAPANICOLAOU, AND O.R. PIRONNEAU, Convection of microstructure and related problems, SIAM J. Appl. Math., 45 (1985), pp. 780-797
19. G. NGUETSENG, A general convergence result for a functional related to the theory of homoge-nization, SIAM J. Math. Anal., 20 (1989), pp. 608-623
20. Y. G. SINAI, Dynamical Systems III, Springer, New York, Heidelberg, Berlin, 1989
21. L. SCHWARTZ, Théorie des Distributions, Hermann, Paris, 1966
22. L. TARTAR, Remarks on homogenization, in Homogenization and Effective Moduli of Material and Media, IMA Vol. Math. Appl., Springer, New York, 1986, pp. 228-246
23. L. TARTAR, Nonlocal effects induced by homogenization, in Partial Differential Equations and the Calculus of Variations, Essays of Mathematical Analysis in Honor of E. De Giorgi, Vol.II, Progr. Nonlinear Differential Equations Appl. 2, Birkhauser, Boston, 1989, pp. 925-938.