|
This article is cited in 5 scientific papers (total in 5 papers)
On an inverse problem for a parabolic equation in a degenerate angular domain
M. T. Jenaliyeva, M. I. Ramazanovb, M. G. Yergaliyevac a Institute of Mathematics and Mathematical Modeling,
125 Pushkin St,
050010 Almaty, Kazakhstan
b E.A. Buketov Karaganda State University,
28 Universitetskaya St,
100028 Karaganda, Kazakhstan
c Al-Farabi Kazakh National University, 71 al-Farabi Ave,
050040 Almaty, Kazakhstan
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.
Keywords and phrases:
coefficient inverse problem, heat equation, degenerate domain, angular domain, parabolic equation.
Received: 21.07.2018 Revised: 24.06.2020
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
Linking options:
https://www.mathnet.ru/eng/emj401 https://www.mathnet.ru/eng/emj/v12/i2/p25
|
|