Abstract:
We consider a coefficient inverse problem for a parabolic equation in a degenerate angular domain when the moving part of the boundary changes linearly. We show that the inverse problem for the homogeneous heat equation with homogeneous boundary conditions has a nontrivial solution up to a constant factor consistent with an additional condition. The boundedness of this solution and this additional condition is proved. Moreover, the solution of the considered inverse problem is found in an explicit form and it is proved that the required coefficient is determined uniquely. It is shown that the obtained nontrivial solution of the inverse problem has no singularities and the additional condition also has no singularities.
This research is funded by the Science Committee of the Ministry of Education and Science of the
Republic of Kazakhstan (grant no. AP09258892, 2021-2023).
Citation:
M. T. Jenaliyev, M. I. Ramazanov, M. G. Yergaliyev, “On an inverse problem for a parabolic equation in a degenerate angular domain”, Eurasian Math. J., 12:2 (2021), 25–38
\Bibitem{DzhRamYer21}
\by M.~T.~Jenaliyev, M.~I.~Ramazanov, M.~G.~Yergaliyev
\paper On an inverse problem for a parabolic equation in a degenerate angular domain
\jour Eurasian Math. J.
\yr 2021
\vol 12
\issue 2
\pages 25--38
\mathnet{http://mi.mathnet.ru/emj401}
\crossref{https://doi.org/10.32523/2077-9879-2021-12-2-25-38}
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This publication is cited in the following 5 articles:
M. T. Jenaliyev, M. G. Yergaliyev, “On initial-boundary value problem for the Burgers equation in nonlinearly degenerating domain”, Applicable Analysis, 103:11 (2024), 2003
Muvasharkhan Jenaliyev, Akerke Serik, Madi Yergaliyev, “Navier–Stokes Equation in a Cone with Cross-Sections in the Form of 3D Spheres, Depending on Time, and the Corresponding Basis”, Mathematics, 12:19 (2024), 3137
U. A. Hoitmetov, “Integration of the loaded general Korteweg-de Vries equation in tne class of rapidly decreasing complex-valued functions”, Eurasian Math. J., 13:2 (2022), 43–54
S. A. Budochkina, H. P. Vu, “On an indirect representation of evolutionary equations in the form of Birkhoff's equations”, Eurasian Math. J., 13:3 (2022), 23–32
T. Sh. Kalmenov, A. K. Les, U. A. Iskakova, “Determination of density of elliptic potential”, Eurasian Math. J., 12:4 (2021), 43–52
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