Locally periodic homogenization

Asymptotic Analysis

Volumn 39, Issue 3-4, 2004, Pages 263-279

  Bencherif Madani A ^a   Pardoux, E ^b  

^a FERHAT ABBAS UNIVERSITY   (Algeria)

^b CNRS   (France)

Author keywords

Diffusion approximation; Homogenization; Parabolic PDE; Poisson equation

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; MATHEMATICAL OPERATORS; POLYNOMIALS;

DIFFUSION APPROXIMATION; HOMOGENIZATION; PARABOLIC EQUATIONS; PARABOLIC PDE;

POISSON EQUATION;

EID: 22044447883     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

1. A. Bencherif-Madani and E. Pardoux, Homogenization of a diffusion with locally periodic coefficients, in: Séminaire de Probabilités XXXVIII, Lecture Notes in Mathematics, 2004, to appear.
2. A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic Analysis of Periodic Structures, North-Holland, Amsterdam, 1978.
3. M. Freidlin, The Dirichlet problem for an equation with periodic coefficients depending on a small parameter, Teor. Primenen. 9 (1964), 133-139.
4. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, 1964.
5. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Revised third printing, Springer-Verlag, New York, 1998.
6. S. Olla, Notes on the Central Limit Theorems for tagged particles and diffusions in random fields, in: Milieux aléatoires, F. Comets and E. Pardoux, eds, Panoramas et Synthèses, Vol. 12, Soc. Math. France, 2002.
7. E. Pardoux, Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: a probabilistic approach, J. Funct. Anal. 167 (1999), 498-520.
8. E. Pardoux and A.Yu. Veretennikov, On the Poisson equation and diffusion approximation, I, Ann. Probab. 29(3) (2001), 1061-1085.
9. E. Pardoux and A.Yu. Veretennikov, On the Poisson equation and diffusion approximation, II, Ann. Probab. 31 (2003), 1166-1192.
10. D.W. Stroock and S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, New York, 1979.