Self-similar Elastic Condition of Filtration Through the Moving Boundary
- Authors: Khabirov S.V.1, Khabirov S.S.1
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Affiliations:
- Mavlyutov Institute of Mechanics Ufa Federal Research Center
- Issue: Vol 40, No 11 (2019)
- Pages: 1950-1958
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/206187
- DOI: https://doi.org/10.1134/S1995080219110167
- ID: 206187
Cite item
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.
About the authors
S. V. Khabirov
Mavlyutov Institute of Mechanics Ufa Federal Research Center
Author for correspondence.
Email: habirov1@anrb.ru
Russian Federation, Ufa, 450054
S. S. Khabirov
Mavlyutov Institute of Mechanics Ufa Federal Research Center
Author for correspondence.
Email: salavat.s.khabirov@gmail.com
Russian Federation, Ufa, 450054