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DOI 10.34229/KCA2522-9664.24.3.7
UDC 517.9: 519.6
V.M. Bulavatsky1


1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

 v_bulav@ukr.net

SOME BOUNDARY-VALUE PROBLEMS CORRESPONDING TO THE MODEL
OF FRACTIONAL-DIFFERENTIAL FILTRATION DYNAMICS IN A FRACTURED-POROUS
MEDIUM UNDER TIME NON-LOCALITY

Abstract. Closed-form solutions of some boundary-value problems of fractional-differential geofiltration dynamics in a fractured-porous medium are obtained for a model with weakly permeable porous blocks. In particular, the direct and inverse boundary-value problems of filtration for the finite thickness layer are solved, the conditions for the existence of their regular solutions are given, and the solution of the problem of filtration dynamics with nonlocal boundary conditions is found. For a particular case of the filtration model, the problem of modeling the anomalous dynamics of filtration pressure fields on a star-shaped graph is considered.

Keywords: mathematical modeling, fractional-differential dynamics of filtration processes, fractured-porous medium, non-classical models, boundary-value problems, inverse problems, problems with non-local conditions, closed-form solutions.


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