UDC 517.9:519.6
1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 v_bulav@ukr.net
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MATHEMATICAL MODELS WITH LOCAL M - DERIVATIVE
AND BOUNDARY-VALUE PROBLEMS OF GEOMIGRATION DYNAMICS
Abstract. In the framework of mathematical models based on the concept of a local M - derivative with respect to a time variable,
statements are made and closed-form solutions of some two-dimensional boundary value problems of convective
and convective-diffusive mass transfer and mass exchange of soluble substances during geofiltration are obtained.
In particular, the inverse retrospective problem of convective diffusion is posed according to the scheme of two-dimensional
geofiltration from an infinite reservoir to drainage, its regularized solution is obtained, and some estimates of convergence are given.
Keywords: mathematical modeling, geomigration, geofiltration, mass transfer, mass exchange, non-classical models,
local M - derivative, problems of convective and convective-diffusive mass transfer, closed form solutions.
FULL TEXT
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