Homogenization of a singularly perturbed parabolic problem in a thick periodic junction of the type 3:2:1

Ukrainian Mathematical Journal

Volumn 52, Issue 11, 2000, Pages 1737-1748

  Mel'nik, T A ^a  

^a TARAS SHEVCHENKO NATIONAL UNIVERSITY OF KYIV   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745950269     PISSN: 00415995     EISSN: 15739376     Source Type: Journal    
DOI: 10.1023/A:1010483205109     Document Type: Article

References (16)

1. V. A. Marchenko and E. Ya. Khruslov, Boundary-Value Problems in Domains with Fine-Grained Boundary [in Russian], Naukova Dumka, Kiev (1974).
2. A. Bensoussan, J. Lions, and G. Papanicolau, Asymptotic Analysis for Periodic Structure, North Nolland, Amsterdam (1978).
3. E. Sanchez-Palencia, Nonhomogeneous Media and Vibration Theory, Springer, Berlin (1980).
4. N. S. Bakhvalov and G. P. Panasenko, Homogenization of Processes in Periodic Media [in Russian], Nauka, Moscow (1984).
5. O. A. Oleinik, G. A. Iosif' yan, and A. S. Shamaev, Mathematical Problems of the Theory of Strongly Inhomogeneous Elastic Media [in Russian], Moscow University, Moscow (1990).
6. I. V. Skrypnik, Methods for Investigation on Nonlinear Elliptic Boundary-Value Problems [in Russian], Nauka, Moscow (1990).
7. V.V. Zhikov, S. M. Kozlov, and O. A. Oleinik, Averaging of Differential Operators [in Russian], Fizmatlit, Moscow (1993).
8. J. Sanchez-Hubert and E. Sanches-Palencia, Vibration and Coupling of Continuous Systems, Springer, Berlin (1989).
9. T. A. Mel'nik, "Homogenization of the Poisson equation in a thick periodic junction," Z. Analysis ihre Anwendungen, 18, No. 4, 953-975 (1999).
10. T. A. Mel'nik and S. A. Nazarov, "Asymptotics of a solution of the spectral Neumann problem in a domain of the 'thick comb' type," Tr. Sem. Petrovsk., 19, 138-174 (1996).
11. T. A. Mel'nik, "Asymptotic analysis of a spectral problem in a periodic thick junction of type 3:2:1," Math. Meth. Appl. Sci., 23, No. 4, 341-346 (2000).
12. G. V. Suzikov and E. Ya. Khruslov, "On propagation of sound waves through thin channels in a reflecting layer," Teor. Funkts. Funkts. Anal. Prilozh., 5, 35-49 (1976).
13. V. P. Kotlyarov and E. Ya. Khruslov, "On a limit boundary condition for a Neumann problem," Teor. Funkts. Funkts. Anal. Prilozh., 10, 83-96 (1970).
14. O. A. Ladyzhenskaya, Boundary-Value Problems in Mathematical Physics [in Russian], Nauka, Moscow (1973).
15. V. P. Mikhailov, Partial Differential Equations [in Russian], Nauka, Moscow (1983).
16. S. A. Nazarov, "Junctions of domains of different limit dimensions with singular degeneration," Tr. Sem. Petrovsk., 18, 1-78 (1995).