| Article |
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| Article name |
About Mathematical Models of Dynamic Processes in Biomaterials with Nanoscale Three-Layer Films |
| Authors |
Kholodovsky S.Y.Doctor of Physics and Mathematics hol47@yandex.ru |
| Bibliographic description |
Kholodovskii S. Ye. About Mathematical Models of Dynamic Processes in Biomaterials with Nanoscale Three-Layer Films // Scholarly Notes Of Transbaikal State University. Series Physics, Mathematics, Engineering, Technology. 2016. Vol. 11, No 4. P. 11-20. DOI:10.21209/2308-8761-2016-11-4-11-20. |
| Section |
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| DOI |
10.21209/2308-8761-2016-11-4-11-20 |
| UDK |
530: 517.956 |
| Article type |
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| Annotation |
The article considers a mathematical model of processes of heat conduction, diffusion, fltration, etc. in the cylindrical regions D = (x £ R) х (y,z £ Q С R2), separated by a film into two half-cylinders D1(x < 0) and D2(x > 0). The film consists of three strongly and weakly permeable layers in an arbitrary combination, in problems of biology it corresponds to the multilayered membranes, the drainage tubes, filter and protective screens, etc. The differential equation in the zones Di can be of any type (elliptic, parabolic, hyperbolic). Using the method of Convolution of Fourier expansions, the solution of boundary value problems with the films is expressed through the solution of a similar classical problem without films. We obtained analytical solutions to specific problems in different areas with three-layer films.
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| Key words |
boundary value problems, nanoscale inclusions, mathematical methods in biology, dynamic processes in inhomogeneous media |
| Article information |
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| References |
1. Kholodovskii S. E. A Method of Convolution of Fourier Expansions as Applied to Solving Boundary Value Problems with Intersecting Interface Lines // Computational Mathematics and Mathematical Physics. 2007. Vol. 47, No. 9. P. 14891495.
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5. Fikhtengol’ts G. M. Kurs differentsial’nogo i integral’nogo ischisleniya. M.: Nauka, 1962. T. 3. 656 s.
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1972. 736 s.
7. Golubeva O.V. Obobshchenie teoremy ob okruzhnosti na fil’tratsionnye techeniya // Izv. AN SSSR. MZhG. 1966. No 1. S. 113-116. |
| Full article | About Mathematical Models of Dynamic Processes in Biomaterials with Nanoscale Three-Layer Films |
