References
- Panasenko G. Method of asymptotic partial decomposition of domain. Math. Models Meth. Appl. Sci. 1998;8:139–156.
- Blanc F, Gipouloux O, Panasenko G, et al. Asymptotic analysis and partial asymptotic decomposition of the domain for Stokes equation in tube structure. Math. Models Meth. Appl. Sci. 1999;9:1351–1378.
- Panasenko G. Partial asymptotic decomposition of domain: Navier--Stokes equation in tube structure. C.R. Acad. Sci. Série IIb. 1998;326:893–898.
- Panasenko G, Pileckas K. Asymptotic analysis of the non-steady Navier--Stokes equations in a tube structure.I. The case without boundary layer-in-time. Nonlinear Anal., Ser. A, Theory, Meth. Appl. 2015;122:125–168. doi:10.1016/j.na.2015.03.008
- Nazarov SA. Elliptic boundary value problems with periodic coefficients in a cylinder. Math. USSR Izvestija. 1982;18:89–98.
- Pileckas K. Weighted Lq-solvability of the steady Stokes system in domains with incompact boundaries. Math. Models Meth. Appl. Sci. 1996;6:97–136.
- Galdi P. An introduction to the mathematical theory of Navier--Stokes equations. New York (NY): Springer; 1994.
- Nazarov SA, Plamenevskiy BA. Elliptic problems in domains with piecewise-smooth boundary. Moscow: Nauka; 1991.
- Ciarlet PG. Plates and junctions in elastic multi-sctructures. An asymptotic analysis. Paris: Masson; 1990. p. 215.
- Argatov II, Nazarov SA. Junction problems of shashlik (skewer) type. C.R. Acad. Sci. Sér. I. 1993;316:1329–1334.
- Kozlov V, Maz’ya V, Movchan A. Asymptotic analysis of fields in multi-structures. New York (NY): Oxford Mathematical Monographs (Oxford Science Publications), The Clarendon Press, Oxford University Press; 1999.
- Le Dret H. Problèmes variationnels dans les multi-domaines: modélisation des Jonctions et applications [Variational problems in multi-domains: modeling of junctions and applications], RMA. Vol. 19. Paris: Masson; 1991.
- Sanchez-Sanchez E. Singularities and junctions in elasticity. In: Nonlinear partial differential equations and their applications. College de France seminar. Vol. 9. Paris: Longman.
- Panasenko G. Asymptotic expansion of the solution of Navier--Stokes equation in a tube structure. C.R. Acad. Sci. S\’{e}r. IIb. 1998;326:867–872.
- Panasenko G. Multi-scale modeling for structures and composites. Dordrecht: Springer; 2005.
- Ladyzhenskaya OA. The mathematical theory of viscous incompressible fluid. New York (NY): Gordon and Breach; 1969.
- Maz’ya V, Slutskii A. Asymptotic analysis of the Navier--Stokes system in a plane domain with thin channels. Asymptotic Anal. 2000;23:59–89.
- Ladyzhenskaya OA. Boundary value problems of mathematical physics. New York (NY): Springer-Verlag; 1985.
- Panasenko G, Pileckas K. Divergence equation in thin-tube structure. Appl. Anal. 2015;94:1450–1459. doi:10.1080/00036811.2014.933476
- Nazarov SA. Elliptic problems in domains with piecewise-smooth boundary. Moscow: Nauka.