Homogenization of periodic non self-adjoint problems with large drift and potential
Grégoire Allaire; Rafael Orive
ESAIM: Control, Optimisation and Calculus of Variations (2007)
- Volume: 13, Issue: 4, page 735-749
- ISSN: 1292-8119
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top- G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal.23 (1992) 1482–1518.
- G. Allaire, Dispersive limits in the homogenization of the wave equation. Annales de la Faculté des Sciences de ToulouseXII (2003) 415–431.
- G. Allaire and Y. Capdeboscq, Homogenization of a spectral problem in neutronic multigroup diffusion. Comput. Methods Appl. Mech. Engrg.187 (2000) 91–117.
- G. Allaire and C. Conca, Bloch wave homogenization and spectral asymptotic analysis. J. Math. Pures Appl.77 (1998) 153–208.
- G. Allaire and F. Malige, Analyse asymptotique spectrale d'un probléme de diffusion neutronique. C. R. Acad. Sci. Paris Sér. I324 (1997) 939–944.
- G. Allaire and R. Orive, On the band gap structure of Hill's equation. J. Math. Anal. Appl.306 (2005) 462–480.
- G. Allaire and A. Piatnitski, Uniform spectral asymptotics for singularly perturbed locally periodic operator. Comm. Partial Differential Equations27 (2002) 705–725.
- 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.
- 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).
- A. Benchérif-Madani and É. Pardoux, Locally periodic homogenization. Asymptot. Anal.39 (2004) 263–279.
- 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.
- A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam (1978).
- Y. Capdeboscq, Homogenization of a diffusion equation with drift. C. R. Acad. Sci. Paris Sér. I327 (1998) 807–812.
- Y. Capdeboscq, Homogenization of a neutronic critical diffusion problem with drift. Proc. Roy. Soc. Edinburgh Sect. A132 (2002) 567–594.
- P. Donato and A. Piatnitski, Averaging of nonstationary parabolic operators with large lower order terms. (2005) (in preparation).
- G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal.20 (1989) 608–623.
- A. Piatnitski, Asymptotic behaviour of the ground state of singularly perturbed elliptic equations. Commun. Math. Phys.197 (1998) 527–551.
- A. Piatnitski, Ground State Asymptotics for Singularly Perturbed Elliptic Problem with Locally Periodic Microstructure. Preprint (2006).
- J. Simon, Compact sets in the space . Ann. Mat. Pura Appl.146 (1987) 65–96.
- S. Sivaji Ganesh and M. Vanninathan, Bloch wave homogenization of scalar elliptic operators. Asymptotic Anal.39 (2004) 15–44.
- M. Vanninathan, Homogenization of eigenvalue problems in perforated domains. Proc. Indian Acad. Sci. Math. Sci.90 (1981) 239–271.