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 Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 5, Pages 832–841 (Mi zvmmf10573)

Inverse problem of determining the right-hand side in a degenerating parabolic equation with unbounded coefficients

V. L. Kamynin

National Research Nuclear University MEPhI, Moscow, Russia

Abstract: Uniqueness and existence theorems for the solution of the inverse problem for a degenerating parabolic equation with unbounded coefficients on a plane in conditions of integral observations are proven. Estimates of the solution with constants explicitly expresses via the input data of the problem are obtained.

Key words: inverse problems, condition of integral observation, degenerating parabolic equations, unbounded coefficients of equation.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 02.à03.21.0005

DOI: https://doi.org/10.7868/S0044466917050040

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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:5, 833–842

Bibliographic databases:

UDC: 519.633

Citation: V. L. Kamynin, “Inverse problem of determining the right-hand side in a degenerating parabolic equation with unbounded coefficients”, Zh. Vychisl. Mat. Mat. Fiz., 57:5 (2017), 832–841; Comput. Math. Math. Phys., 57:5 (2017), 833–842

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. L. Kamynin, “On the Stabilization to Zero of the Solutions of the Inverse Problem for a Degenerate Parabolic Equation with Two Independent Variables”, Math. Notes, 101:6 (2017), 974–983
2. E. I. Azizbayov, Ya. T. Mehraliyev, “Nonlocal inverse problem for determination of time derivative coefficient in a second-order parabolic equation”, Adv. Differ. Equ. Control Process., 19:1 (2018), 15–36
3. V. L. Kamynin, “Asymptotic behavior of solutions of inverse problems for degenerate parabolic equations”, Differ. Equ., 54:5 (2018), 633–647
4. A. I. Prilepko, V. L. Kamynin, A. B. Kostin, “Inverse source problem for parabolic equation with the condition of integral observation in time”, J. Inverse Ill-Posed Probl., 26:4 (2018), 523–539
5. V. L. Kamynin, “On inverse problems for strongly degenerate parabolic equations under the integral observation condition”, Comput. Math. Math. Phys., 58:12 (2018), 2002–2017
6. N. V. Martemyanova, “Nonlocal inverse problem to find unknown multipliers in right part of Lavrentev–Bitsadze equation”, Russian Math. (Iz. VUZ), 64:1 (2020), 40–57
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