Article |
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Article name |
On the Solution of the Dirichlet Problem in a Piecewise Homogeneous Band with the Two-layer Film Inclusion |
Authors |
Kuznetsova N.V. Senior Teacher, pestryakovi@mail.ru |
Bibliographic description |
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Section |
Scientific Research |
UDK |
517.956 |
DOI |
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Article type |
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Annotation |
Consider the Dirichlet problem for the Laplace equation in a piecewise homogeneous band
D(x ∈ R) = D1(x < 0) ∪ D2(x > 0), 0 < y < π of permeability ki in the Di. Regions Di are
separated by an infinitely thin two-layer film x = 0consisting of a hard and low permeability
layers. Solution of the problem is expressed in terms of the classical solution of the Dirichlet
problem in a homogeneous band without film.
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Key words |
boundary value problems in the band, two-layer film inclusion, strongly
permeable film, weakly permeable film, method of convolution of Fourier expansions. |
Article information |
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References |
1. Vasil’ev B. A. Ploskaya statsionarnaya zadacha teorii teploprovodnosti dlya sostavnoi
klinovidnoi oblasti // Differents. uravneniya. 1984. T. 20. № 3. S. 530–533.
2. Gurevich A. V., Krylov A. L., Topor D. N. reshenie ploskikh zadach gidrodinamiki
poristykh sred vblizi razryvnykh narushenii metodom kompleksnogo potentsiala // Dan SSSR.
1988. T. 298. № 4. S. 846–850.
3. Krutitskii P. A., Prozorov K. V. K zadache dlya uravneniya Gel’mgol’tsa vne razrezov
na ploskosti s zadaniem usloviya Dirikhle i usloviya s kosoi proizvodnoi na raznykh storonakh
razrezov // Differents uravneniya. 2011. T. 47. № 9. S. 1269–1283.
4. Nutchina-Pestryakova N. V. O reshenii zadach Dirikhle v kusochno-odnorodnoi
poluploskosti s dvukhsloinym plenochnym vklyucheniem // Matematicheskii analiz i ego
prilozheniya. 2011. Vyp. 10. Chita: ZabGGPU. S. 41?49.
5. Kholodochskii S. E. Metod svertyvniya razlozhenii Fur’e v reshenii kraevykh zadach
s peresekayushchimisya liniyami sopryazheniya // Zhurnal vychislitel’nyi matematiki i
matematicheskoi fiziki. 2007. T. 47. № 9. S. 1550–1556.
6. Kholodovskii S. E. Metod svertyvaniya razlozhenii Fur’e. Sluchai treshchiny (zavesy)
v neodnorodnom prostranstve // Differents. uraneniya. 2009. T. 45. № 8. S. 1204–1208. |
Full article | On the Solution of the Dirichlet Problem in a Piecewise Homogeneous Band with the Two-layer Film Inclusion |