Lobachevskii Journal of Mathematics

, Volume 40, Issue 11, pp 1950–1958

# Self-similar Elastic Condition of Filtration Through the Moving Boundary

• S. V. Khabirov
• S. S. Khabirov
Article

## 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.

## Keywords and phrases

elastic filtration moving boundary invariant solution Weber equation boundary-value problem asymptotic of solution

## Notes

### 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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