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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 209, Number 1, Pages 184–202
DOI: https://doi.org/10.4213/tmf10113 (Mi tmf10113) 		 
On a free boundary problem for the relaxation transfer equation

J. O. Takhirov, M. T. Umirkhonov

Romanovskiy Institute of Mathematcs, Academy of Sciences of the~Republic of Uzbekistan, Tashkent, Uzbekistan
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DOI: https://doi.org/10.4213/tmf10113
Abstract: We study the free boundary problem with no initial conditions for a third-order relaxation transfer equation. First, we reduce the problem to a second-order equation and prove the uniqueness theorem. The solution of this problem is constructed as a limit of solutions of corresponding problems that are first reduced to a Stefan-type problem with initial conditions. Free boundary behavior is explored.
Keywords: relaxation, transfer, free boundary, a priori estimate, existence and uniqueness of solution.
Received: 18.04.2021
Revised: 22.05.2021
English version:
Theoretical and Mathematical Physics, 2021, Volume 209, Issue 1, Pages 1473–1489
DOI: https://doi.org/10.1134/S0040577921100093
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Document Type: Article
Language: Russian
Citation: J. O. Takhirov, M. T. Umirkhonov, “On a free boundary problem for the relaxation transfer equation”, TMF, 209:1 (2021), 184–202; Theoret. and Math. Phys., 209:1 (2021), 1473–1489
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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