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 Mat. Zametki, 2015, Volume 98, Issue 5, Pages 710–724 (Mi mz10778)

On the Solvability of the Inverse Problem for Determining the Right-Hand Side of a Degenerate Parabolic Equation with Integral Observation

V. L. Kamynin

National Engineering Physics Institute "MEPhI", Moscow

Abstract: Existence and uniqueness theorems and theorems on stability under perturbations of the input data for solutions of the inverse problem for a degenerate parabolic equation in the plane with integral observation are obtained. The cases of bounded and unbounded coefficients are studied. Estimates of the solution with constants explicitly written out in terms of the input data of the problem are obtained.

Keywords: degenerate parabolic equation, solvability of the inverse problem, stability of solutions, perturbation of the input data, integral observation, maximum principle.

DOI: https://doi.org/10.4213/mzm10778

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English version:
Mathematical Notes, 2015, 98:5, 765–777

Bibliographic databases:

UDC: 517.95

Citation: V. L. Kamynin, “On the Solvability of the Inverse Problem for Determining the Right-Hand Side of a Degenerate Parabolic Equation with Integral Observation”, Mat. Zametki, 98:5 (2015), 710–724; Math. Notes, 98:5 (2015), 765–777

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz10778
• https://doi.org/10.4213/mzm10778
• http://mi.mathnet.ru/eng/mz/v98/i5/p710

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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. V. L. Kamynin, “Inverse problem of determining the right-hand side in a degenerating parabolic equation with unbounded coefficients”, Comput. Math. Math. Phys., 57:5 (2017), 833–842
3. S. A. Zolotykh, V. A. Stukopin, “Asymptotics of Eigenvalues of Simple Multiloop Banded Toeplitz Matrices of a Special Type”, Math. Notes, 102:4 (2017), 575–579
4. V. L. Kamynin, T. I. Bukharova, “On inverse problem of determination the right-hand side term in higher order degenerate parabolic equation with integral observation in time”, VI International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 937, IOP Publishing Ltd, 2017, UNSP 012018
5. V. L. Kamynin, T. I. Bukharova, “Inverse problems of determination of the right-hand side term in the degenerate higher-order parabolic equation on a plane”, Numerical Analysis and Its Applications (NAA 2016), Lecture Notes in Computer Science, 10187, eds. I. Dimov, I. Farago, L. Vulkov, Springer International Publishing Ag, 2017, 391–397
6. V. L. Kamynin, T. I. Bukharova, “On stability of the solutions of inverse problem for determining the right-hand side of a degenerate parabolic equation with two independent variables”, V International Conference on Problems of Mathematical and Theoretical Physics and Mathematical Modelling, Journal of Physics Conference Series, 788, IOP Publishing Ltd, 2017, UNSP 012050
7. V. I. Vasiliev, L. Su, “Numerical method for solving boundary inverse problem for one-dimensional parabolic equation”, Matematicheskie zametki SVFU, 24:2 (2017), 108–117
8. V. L. Kamynin, “Asymptotic behavior of solutions of inverse problems for degenerate parabolic equations”, Differ. Equ., 54:5 (2018), 633–647
9. 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
10. 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
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