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Mathematical Models with Local M-Derivative and Boundary-Value Problems of Geomigration Dynamics

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Abstract

Within the framework of mathematical models based on the concept of a local M-derivative with respect to time variable, statements are made and closed-form solutions to some two-dimensional boundary-value problems of convective and convective-diffusion mass transfer and mass exchange of soluble substances during geofiltration are obtained. In particular, an 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.

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Authors and Affiliations

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

    V. M. Bulavatsky

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  1. V. M. Bulavatsky
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Correspondence to V. M. Bulavatsky.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 4, July–August, 2021, pp. 70–87.

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Bulavatsky, V.M. Mathematical Models with Local M-Derivative and Boundary-Value Problems of Geomigration Dynamics. Cybern Syst Anal 57, 563–577 (2021). https://doi.org/10.1007/s10559-021-00381-7

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  • DOI: https://doi.org/10.1007/s10559-021-00381-7

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