UDC 517.954:532.546
1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 v_bulav@ukr.net
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CLOSED SOLUTIONS OF SOME BOUNDARY-VALUE PROBLEMS
OF FILTRATION-CONSOLIDATION DYNAMICS
WITHIN FRACTIONAL-FRACTAL APPROACH
Abstract. The autor constructs a fractional-fractal mathematical model of the dynamics of the process of filtration consolidation of a soil media,
a model of the dynamics of the process of filtration consolidation of massifs of fractal structure, taking into account the creep of the soil skeleton
(direct and inverse retrospective problems) and a fractional-fractal mathematical model of the dynamics of the process of filtration consolidation
of saturated saline solutions of soil media. Within the framework of these models, statements have been made and closed solutions have been obtained
for some boundary-value problems, one-dimensional with respect to the geometric variable, on the consolidation of water-saturated soil massifs
of fractal structure under time nonlocality of the consolidation process.
Keywords: mathematical modeling, filtration-consolidation processes, non-classical models, soil media of fractal structure, dynamics, fractional-fractal approach, direct and inverse problems, closed solutions.
FULL TEXT
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