Bulavatsky V.M.
Closed solutions of some boundary-value problems of filtration-consolidation dynamics within fractional-fractal approach

The autor constructs a fractured-fractal mathematical model of the dynamics of the process of filtration consolidation of a soil medium, a model of the dynamics of the process of filtration consolidation of massifs of fractal structure, taking into account creep of the soil skeleton (direct and inverse retrospective problems), and a fractured-fractal mathematical model of the dynamics of the process of filtration consolidation of soil media saturated with saline solutions. 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 compaction process. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: closed solutions, direct and inverse problems, dynamics, filtration-consolidation processes, fractured-fractal approach, mathematical modeling, nonclassical models, soil media of fractal structure, Boundary value problems, Dynamics, Filtration, Fracture, Inverse problems, Soils, Closed solutions, Compaction process, Fractal approach, Fractal structures, Geometric variables, Nonlocalities, Saline solutions, Water saturated soils, Fractals

Cite:
Bulavatsky V.M. (2021). Closed solutions of some boundary-value problems of filtration-consolidation dynamics within fractional-fractal approach. Cybernetics and Systems Analysis, 57 (3), 53–66. doi: https://doi.org/10.1007/s10559-021-00363-9 http://jnas.nbuv.gov.ua/article/UJRN-0001239407 [In Russian].