Homogenization of periodic non self-adjoint problems with large drift and potential

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 13, Issue 4, 2007, Pages 735-749

  Allaire, Grégoire ^a   Orive, Rafael ^b  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

Convection diffusion; Homogenization; Non self adjoint operators; Periodic medium

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; HOMOGENIZATION METHOD; MATHEMATICAL OPERATORS;

NON SELF-ADJOINT OPERATORS; PERIODIC MEDIUMS;

PROBLEM SOLVING;

EID: 38949131935     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2007030     Document Type: Article

References (21)

1. G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992) 1482-1518.
2. G. Allaire, Dispersive limits in the homogenization of the wave equation. Annales de la Faculté des Sciences de Toulouse XII (2003) 415-431.
3. G. Allaire and Y. Capdeboscq, Homogenization of a spectral problem in neutronic multigroup diffusion. Comput. Methods Appl. Mech. Engrg. 187 (2000) 91-117.
4. G. Allaire and C. Conca, Bloch wave homogenization and spectral asymptotic analysis. J. Math. Pures Appl. 77 (1998) 153-208.
5. G. Allaire and F. Malige, Analyse asymptotique spectrale d'un probléme de diffusion neutronique. C. R. Acad. Sci. Paris Sér. I 324 (1997) 939-944.
6. G. Allaire and R. Orive, On the band gap structure of Hill's equation. J. Math. Anal. Appl. 306 (2005) 462-480.
7. G. Allaire and A. Piatnitski, Uniform spectral asymptotics for singularly perturbed locally periodic operator. Comm. Partial Differential Equations 27 (2002) 705-725.
8. G. Allaire, Y. Capdeboscq, A. Piatnitski, V. Siess and M. Vanninathan, Homogenization of periodic systems with large potentials. Arch. Rational Mech. Anal. 174 (2004) 179-220.
9. P.H. Anselone, Collectively compact operator approximation theory and applications to integral equations. Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1971).
10. A. Benchérif-Madani and É. Pardoux, Locally periodic homogenization. Asymptot. Anal. 39 (2004) 263-279.
11. A. Benchérif-Madani and É. Pardoux, Homogenization of a diffusion with locally periodic coefficients. Séminaire de Probabilités XXXVIII Lect. Notes Math. 1857 (2005) 363-392.
12. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam (1978).
13. Y. Capdeboscq, Homogenization of a diffusion equation with drift. C. R. Acad. Sci. Paris Sér. I 327 (1998) 807-812.
14. Y. Capdeboscq, Homogenization of a neutronic critical diffusion problem with drift. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002) 567-594.
15. P. Donato and A. Piatnitski, Averaging of nonstationary parabolic operators with large lower order terms. (2005) (in preparation).
16. G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608-623.
17. A. Piatnitski, Asymptotic behaviour of the ground state of singularly perturbed elliptic equations. Commun. Math. Phys. 197 (1998) 527-551.
18. A. Piatnitski, Ground State Asymptotics for Singularly Perturbed Elliptic Problem with Locally Periodic Micro structure. Preprint (2006).
19. P(O, T; B). Ann. Mat. Pura Appl. 146 (1987) 65-96.
20. S. Sivaji Ganesh and M. Vanninathan, Bloch wave homogenization of scalar elliptic operators. Asymptotic Anal. 39 (2004) 15-44.
21. M. Vanninathan, Homogenization of eigenvalue problems in perforated domains. Proc. Indian Acad. Sci. Math. Sci. 90 (1981) 239-271.