The Global-in-Time Existence of a Classical Solution for Some Free Boundary Problem
- Authors: Meirmanov A.M.1, Galtsev O.V.1, Galtseva O.A.1
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Affiliations:
- Belgorod State University
- Issue: Vol 60, No 2 (2019)
- Pages: 325-333
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172348
- DOI: https://doi.org/10.1134/S0037446619020137
- ID: 172348
Cite item
Abstract
We consider the problem with free (unknown) boundary for the one-dimensional diffusion–convection equation. The unknown boundary is found from the additional condition on the free boundary. A dilation of the variables reduces the problem to an initial-boundary value problem for a strictly parabolic equation with unknown coefficients in the known domain. These coefficients are found from an additional boundary condition, which makes it possible to construct a nonlinear operator whose fixed points define the solution to the initial problem.
About the authors
A. M. Meirmanov
Belgorod State University
Author for correspondence.
Email: meirmanov@bsu.edu.ru
Russian Federation, Belgorod
O. V. Galtsev
Belgorod State University
Author for correspondence.
Email: galtsev_o@bsu.edu.ru
Russian Federation, Belgorod
O. A. Galtseva
Belgorod State University
Author for correspondence.
Email: galtseva@bsu.edu.ru
Russian Federation, Belgorod