Partial asymptotic decomposition of the domain for the diffusion–discrete absorption
G. P. Panasenko

References
1.	Bakhvalov N. S., “Osrednenie differentsialnykh uravnenii s chastnymi proizvodnymi s bystro ostsilliruyuschimi koeffitsientami”, Dokl. AN SSSR, 221:3 (1975), 516–519
2.	Born M., Khuan Kun, Dinamicheskaya teoriya kristallicheskikh reshetok, IL, M., 1958, 488 pp.
3.	Ilin A. M., “Raznostnaya skhema dlya differentsialnogo uravneniya s malym parametrom pri starshikh proizvodnykh”, Mat. zametki, 6:2 (1969), 237–248
4.	Kozlov S. M., “Usrednenie raznostnykh skhem”, Mat. cb., 129(171):3 (1986), 338–357
5.	Nazarov S. A., Paukshto M. V., Diskretnye modeli i osrednenie v zadachakh teorii uprugosti, Izd-vo Leningrad. un-ta, L., 1984
6.	Shenoy V. B., Miller R., Tadmor E. B., Rodney D., Phillips R., Ortiz M., “An adaptive finite element approach to atomic-scale mechanics – the quasicontinuum method”, J. Mech. Phys. Solids, 47:3 (1999), 611–642
7.	Bessonov N., Volpert V., Dynamic models of plant growth. Mathematics and Mathematical Modelling, Publibook, Paris, 2006, 68 pp.
8.	Betoue Etoughe M., Panasenko G., “Partial homogenization of discrete models”, Appl. Anal., 87:12 (2008), 1425–1442
9.	Blanc X., Le Bris C., Lions P.-L., “From molecular models to continuum mechanics”, Arch. Ration. Mech. Anal., 164:4 (2002), 341–381
10.	Blanc X., Le Bris C., Legoll F., “Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics”, Math. Model. Numer. Anal., 39:4 (2005), 797–826
11.	Caillerie D., Muorad A., Raoult A., “Discrete homogenization in graphene sheet modeling”, J. Elasticity, 84:1 (2006), 33–68
12.	Kunin I. A., Elastic media with microstructure, v. I, Springer Ser. in Solid-State Sciences, 26, One-dimensional models, Springer-Verlag, Berlin–New York, 1982, 291 pp.      ; Elastic media with microstructure, v. II, Springer Ser. in Solid-State Sciences, 44, Three-dimensional models, Springer-Verlag, Berlin–New York, 1983, 272 pp.
13.	Kurbatova P., Panasenko G., Volpert V., “Asymptotic numerical analysis of the diffusion-discrete absorption equation”, Math. Meth. Appl. Sci., 35 (2012), 438–444
14.	Orive R., Zuazua E., “Finite difference approximation of homogenization problems for elliptic equations”, Multiscale Model. Simul., 4:1 (2005), 36–87, (electronic)
15.	Panasenko G., Multi-scale modeling for structures and composites, Springer, Dordrecht, 2005, 398 pp.
16.	Panasenko G., “The partial homogenization: continuous and semi-discretized versions”, Math. Models Methods Appl. Sci., 17:8 (2007), 1183–1209
17.	Piatnitski A., Remy E., “Homogenization of elliptic difference operators”, SIAM J. Math. Anal., 33:1 (2001), 53–83