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Self-similar Elastic Condition of Filtration Through the Moving Boundary

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Abstract

We consider the one-dimensional problem of the elastic filtration of a fluid though the moving boundary. The boundary conditions are introduced so that the problem be invariant. The invariant problem is reduced to a overdetermine boundary task for the Weber equation. Exact solutions are found. The asymptotic of a solution in infinite point determines the invariant law of a filtration according to the given boundary conditions. There is a connection between overdetermine invariant boundary conditions for any invariant law of a filtration.

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Funding

The work is performed according to the Russian Government Program (project no. 0246-2019-0052) and was supported by the Russian Foundation for Basic Research (project no. 18-29-10071).

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Authors and Affiliations

  1. Mavlyutov Institute of Mechanics Ufa Federal Research Center, Russian Academy of Sciences, Ufa, 450054, Russia

    S. V. Khabirov & S. S. Khabirov

Authors
  1. S. V. Khabirov
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  2. S. S. Khabirov
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Correspondence to S. V. Khabirov or S. S. Khabirov.

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Submitted by A. V. Lapin

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Khabirov, S.V., Khabirov, S.S. Self-similar Elastic Condition of Filtration Through the Moving Boundary. Lobachevskii J Math 40, 1950–1958 (2019). https://doi.org/10.1134/S1995080219110167

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  • DOI: https://doi.org/10.1134/S1995080219110167

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