Article
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
Section
DOI
UDK 517.956
Article type
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.
Key words boundary value problems in the band, two-layer film inclusion, strongly permeable film, weakly permeable film, method of convolution of Fourier expansions.
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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 articleOn the Solution of the Dirichlet Problem in a Piecewise Homogeneous Band with the Two-layer Film Inclusion