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On a free boundary problem for the relaxation transfer equation

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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.

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Authors and Affiliations

  1. Romanovsky Institute of Mathematics, Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan

    J. O. Takhirov & M. T. Umirkhonov

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  1. J. O. Takhirov
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  2. M. T. Umirkhonov
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Correspondence to J. O. Takhirov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 209, pp. 184–202 https://doi.org/10.4213/tmf10113.

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Takhirov, J.O., Umirkhonov, M.T. On a free boundary problem for the relaxation transfer equation. Theor Math Phys 209, 1473–1489 (2021). https://doi.org/10.1134/S0040577921100093

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