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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 2, Pages 419–428
DOI: https://doi.org/10.33048/smzh.2019.60.213 (Mi smj3085) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The global-in-time existence of a classical solution for some free boundary problem

A. M. Meirmanov, O. V. Galtsev, O. A. Galtseva

Belgorod State University, Belgorod, Russia
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DOI: https://doi.org/10.33048/smzh.2019.60.213
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.
Keywords: free boundary problem, diffusion-convection equation, fixed point method, a priori estimate.
Received: 29.05.2018
Revised: 15.12.2018
Accepted: 19.12.2018
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 2, Pages 325–333
DOI: https://doi.org/10.1134/S0037446619020137
Bibliographic databases:
Document Type: Article
UDC: 517.9:531:573
MSC: 35R30
Language: Russian
Citation: A. M. Meirmanov, O. V. Galtsev, O. A. Galtseva, “The global-in-time existence of a classical solution for some free boundary problem”, Sibirsk. Mat. Zh., 60:2 (2019), 419–428; Siberian Math. J., 60:2 (2019), 325–333
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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