Article
Article name On the Solution of Regional Value Problems for the Poisson Equation in Flat Areas Bounded with Strongly and Weakly Permeable Films Connected in Series
Authors Kholodovsky S.Y. Doctor of Physics and Mathematics, hol47@yandex.ru
Bibliographic description
Section Scientific Research
UDK 517.956
DOI
Article type
Annotation The problem for the Laplace operator in the quadrant with bounded strongly and weakly permeable films. Using the method of convolution of Fourier expansions the solution of the problem expressed in terms of the mixed problem in this quadrant of the classical boundary conditions of the first and second kind. It is shown that the method of conformal mappings can extend the class of domains bounded system strongly and weakly permeable films.
Key words boundary value problems, the boundaries of the film, strongly permeable film, weakly permeable film, the method of convolution of Fourier expansions.
Article information
References 1. Kholodovskii S. E. O reshenii kraevykh zadach v poluprostranstve, ogranichennom mnogosloinoi plenkoi // Uchenye zapiski ZabGGPU. Ser. ¾Fizika, matematika, tekhnika, tekhnologiya¿. 2011. № 3(38). S. 160–164. 2. Kholodovskii S. E. Reshenie kraevykh zadach v polutsilindrakh s osnovaniem v vide dvukhsloinoi plenki // Tezisy dokladov Mezhdunar. konf., posvyash. 105-letiyu so dnya rozhdeniya S. L. Soboleva. Differentsial’nye uravneniya, funktsional’nye prostranstva, teoriya priblizhenii. Institut matematiki im. S. L. Soboleva SO RAN. Novosibirsk, 2013. S. 283. 3. Kholodovskii S. E. Metod svertyvaniya razlozhenii Fur’e. Sluchai obobshchyonnykh uslovii sopryazheniya tipa treshchiny (zavesy) v kusochno-neodnorodnykh sredakh // Differentsial’nye uravneniya. 2009. T. 45. № 6. S. 855–859. 4. Kholodovskii S. E. Metod svertyvaniya razlozhenii Fur’e. Sluchai treshchiny (zavesy) v neodnorodnom prostranstve // Differentsial’nye uravneniya. 2009. T. 45. № 8. S. 1204–1208. 5. Tikhonov A. N., Samarskii A. A. Uravneniya matematicheskoi fiziki. M.: Nauka, 1972.
Full articleOn the Solution of Regional Value Problems for the Poisson Equation in Flat Areas Bounded with Strongly and Weakly Permeable Films Connected in Series