| Article |
|---|
| Article name |
Solving Boundary Value Problems for the Poisson Equation on a Half-Plane Bounded by a Film |
| Authors |
Kholodovsky S.Y. Doctor of Physics and Mathematics, hol47@yandex.ru |
| Bibliographic description |
Kholodovskii S. Ye. Solving Boundary Value Problems for the Poisson Equation on a HalfPlane Bounded by a Film // Scholarly Notes of Transbaikal State University. 2019. Vol. 14, No 3. PP. 24-30. DOI: 10.21209/2308-8761-2019-14-3-24-30. 30 |
| Section |
PROBLEMS OF MATHEMATICAL PHYSICS. ANALYTICAL METHODS |
| UDK |
517.956 |
| DOI |
10.21209/2308-8761-2019-14-3-24-30 |
| Article type |
|
| Annotation |
Boundary-value problems for the Poisson equation on half-planes with inhomogeneous boundary conditions of the type of weakly and strongly permeable films on the boundary are considered. The formulas expressing solutions to the problems considered through solutions of the classical problems of Dirichlet and Neumann, respectively, on a half-plane, are derived. The theorems of existence and uniqueness are proved.
|
| Key words |
boundary value problems, weakly permeable film, strongly permeable film, method of convolution of Fourier expansions |
| Article information |
|
| References |
1. Vasil’ev B. A. Ploskaya stacionarnaya zadacha teorii teploprovodnosti dlya sostavnoj klinovidnoj oblasti // Differencial’nye uravneniya. 1984. T. 20, № 3. S. 530-533.
2. Holodovskij S. E. O mnogoslojnyh plyonkah na granice poluprostranstva // Matematicheskie zametki. 2016. T. 99, vyp. 3. S. 421-427.
3. Holodovskij S. E. Reshenie kraevoj zadachi dlya uravneniya Laplasa v kusochno- odnorodnoj poluploskosti, ogranichennoj slabopronicaemoj plyonkoj // Obozrenie prikladnoj i promyshlennoj matematiki. 2018. T. 25, vyp. 2. S. 187-188.
4. Holodovskij S. E. Metod svyortyvaniya razlozhenij Fur’e v reshenii kraevyh zadach s peresekayushchimisya liniyami sopryazheniya // ZHurnal vychislitel’noj matematiki i matematicheskoj fiziki. 2007. T. 47, № 9. S. 1550-1556.
5. Holodovskij S. E. Metod svyortyvaniya razlozhenij Fur’e. Sluchaj treshchiny (zavesy) v neodnorodnom prostranstve // Differencial’nye uravneniya. 2009. T. 45, № 8. S. 1204-1208.
6. Arsenin V. Ya. Metody matematicheskoj fiziki i special’nye funkcii. M.: Nauka, 1974. 735 s.
7. Fihtengol’c G. M. Kurs differencial’nogo i integral’nogo ischisleniya. M.: Nauka, 1962. T. 3. 656 s. |
| Full article | Solving Boundary Value Problems for the Poisson Equation on a Half-Plane Bounded by a Film |
