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

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

DOI: 10.4213/tmf10113

 English version: Theoretical and Mathematical Physics, 2021, 209:1, 1473–1489

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