Self-similar Elastic Condition of Filtration Through the Moving Boundary

Self-similar Elastic Condition of Filtration Through the Moving Boundary

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 a...

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Veröffentlicht in:Lobachevskii journal of mathematics 2019-11, Vol.40 (11), p.1950-1958
Hauptverfasser: Khabirov, S. V., Khabirov, S. S.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Boundary conditions
Filtration
Geometry
Invariants
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Self-similarity
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container_end_page 1958
container_issue 11
container_start_page 1950
container_title Lobachevskii journal of mathematics
container_volume 40
creator Khabirov, S. V.
Khabirov, S. S.
description 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.
doi_str_mv 10.1134/S1995080219110167
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source Springer Nature - Complete Springer Journals
subjects Algebra
Analysis
Boundary conditions
Filtration
Geometry
Invariants
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Self-similarity
title Self-similar Elastic Condition of Filtration Through the Moving Boundary
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