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About Mathematical Models of Dynamic Processes in Biomaterials with Nanoscale Three-Layer Films
Authors: Svyatoslav Ye. Kholodovskii
Number of views: 394
The article considers a mathematical model of processes of heat conduction, diffusion,
fltration, etc. in the cylindrical regions D = (x 2 R) (y; z 2 Q 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.