Some results in homogenization tackling memory effects

Asymptotic Analysis

Volumn 15, Issue 3-4, 1997, Pages 229-259

  Alexandre, Radjesvarane ^a  

^a UNIVERSITÉ D'ORLÉANS   (France)

Author keywords

Homogenization; Hyperbolic systems; Linear differential equations; Memory effects; Neutronic theory; Pseudodifferential operators; Transport equations; Transverse oscillations; Volterra equation

Indexed keywords

EID: 0007215297     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: 10.3233/asy-1997-153-402     Document Type: Article

References (20)

1. G. Allaire, Homogenization and two scale convergence, SIAM J. Math. Anal. 23(6) (1992), 1482-1518.
2. Y. Amirat, K. Hamdache and A. Ziani, Homogénéisation d'équations hyperboliques du premier ordre et applications aux écoulements miscibles en milieu poreux, Ann. Inst. Henri Poincaré, Anal. Non Lin. 6(5) (1989), 397-417.
3. Y. Amirat, K. Hamdache and A. Ziani, Homogenization of parametrized families of hyperbolic problems, Proc. Roy. Soc. Edinburgh 120A (1992), 199-221.
4. Y. Amirat, K. Hamdache and A. Ziani, Some results on homogenization of convection diffusion equations, Arch. Rat. Mech. Anal. 114 (1991), 155-178.
5. N. Antonic, Memory effects in homogenization. Linear second order equations, Research Report 92-NA-005, C.N.A. Carnegie Mellon Univ., Pittsburgh, PA, 1992.
6. A. Bensoussan, J.L. Lions and G.C. Papanicolaou, Boundary layers and homogenization of transport proceses, J. Publ. RIMS, Kyoto Univ. 15 (1979), 53-157.
7. T.A. Burton, Volterra and Integral Equations, Academic Press, 1983.
8. C. Cercignani, Boltzmann Equation and its Applications, Springer, 1985.
9. R. Dautray and J.L. Lions, Calcul Scientifique pour les Sciences et les Techniques, Vols 1 and 3, Masson, Paris, 1983.
10. R.J. DiPerna and P.L. Lions, Global weak solutions of Vlasov-Maxwell system, Com. Pure Appl. Math. 42 (1989), 729-757.
11. p regularity of velocity averages, Ann. Inst. Henri Poincaré Anal. Non Lin. 8(3,4) (1991), 271-287.
12. W. E, Homogenization of linear and non linear transport equations, Com. Pure Appl. Math. 45(3) (1992), 301-326.
13. F. Golse, Remarques sur l'homogénéisation des équations de transport, C. R. Acad. Sci. Paris, Série I 305 (1987), 801-804.
14. G. N'Guetseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. Math. Anal. 29(3) (1989), 608-623.
15. L. Hormander, The Analysis of Linear Partial Differential Operators. I, N 256, Springer, 1980.
16. M.L. Mascarenhas, A linear homogenization problem with time dependant coefficient, Trans. AMS 281(1) (1984), 179-1985.
17. L. Tartar, Non local effects induced by homogenization, in: P.D.E. and Calculus of Variations. Essays in Honour of E. De Giorgi, Vol. 2, Birkhäuser, 1989, pp. 925-938.
18. L. Tartar, Memory effects and homogenization, Arch. Rat. Mech. Anal. 111 (1990), 121-133.
19. L. Tartar, Remarks on homogenization, in: Homogenization and Effective Moduli of Materials and Media, J.L. Ericksen et al., eds, Springer, New York, 1986.
20. L. Tartar, Compensated Compactness and Applications to Partial Differential Equations, Heriott Watt Symposium, Vol. IV, Pitman, New York, 1979.