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Matematicheskie Zametki, 2020, Volume 107, Issue 2, Pages 229–240
DOI: https://doi.org/10.4213/mzm12409 (Mi mzm12409) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On the Global-in-Time Existence of a Generalized Solution to a Free-Boundary Problem

A. M. Meirmanova, O. A. Galtsevab, V. E. Seldemirovb

a Moscow Technical University of Communications and Informatics
b National Research University "Belgorod State University"
Full-text PDF (498 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm12409
Abstract: A problem with free (unknown) boundary for a one-dimensional diffusion-convection equation is considered. The unknown boundary is found from an additional condition on the free boundary. By the extension of the variables, the problem in an unknown domain is reduced to an initial boundary-value problem for a strictly parabolic equation with unknown coefficients in a known domain. These coefficients are found from an additional boundary condition that enables the construction of a nonlinear operator whose fixed points determine a solution of the original problem.
Keywords: free-boundary problems, diffusion-convection equation, fixed-point method, a priori estimates.
Received: 12.04.2019
English version:
Mathematical Notes, 2020, Volume 107, Issue 2, Pages 274–283
DOI: https://doi.org/10.1134/S0001434620010277
Bibliographic databases:
Document Type: Article
UDC: 517.958:531.72
Language: Russian
Citation: A. M. Meirmanov, O. A. Galtseva, V. E. Seldemirov, “On the Global-in-Time Existence of a Generalized Solution to a Free-Boundary Problem”, Mat. Zametki, 107:2 (2020), 229–240; Math. Notes, 107:2 (2020), 274–283
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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