ON AN INVERSE PROBLEM FOR A PARABOLIC EQUATION IN A DEGENERATE ANGULAR DOMAIN
Jenaliyev M.T. Ramazanov M.I. Yergaliyev M.G.
2021L.N. Gumilyov Eurasian National University
Eurasian Mathematical Journal
2021#12Issue 201 - 23 pp.
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.
angular domain , coefficient inverse problem , degenerate domain , heat equation , parabolic equation
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Institute of Mathematics and Mathematical Modeling 125 Pushkin St, Almaty, 050010, Kazakhstan
E.A. Buketov Karaganda State University 28 Universitetskaya St, Karaganda, 100028, Kazakhstan
Al-Farabi Kazakh National University, Institute of Mathematics and Mathematical Modeling, 71 al-Farabi Ave, 125 Pushkin St, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling 125 Pushkin St
E.A. Buketov Karaganda State University 28 Universitetskaya St
Al-Farabi Kazakh National University
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