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 Mat. Zametki, 2015, Volume 97, Issue 3, Pages 368–381 (Mi mz10499)

The Inverse Problem of the Simultaneous Determination of the Right-Hand Side and the Lowest Coefficient in Parabolic Equations with Many Space Variables

V. L. Kamynin

National Engineering Physics Institute "MEPhI", Moscow

Abstract: We obtain existence and uniqueness theorems for the solution of the inverse problem of the simultaneous determination of the right-hand side and the lowest coefficient in multidimensional parabolic equations with integral observation. We give an estimate of the maximum of the modulus of unknown coefficients with constants explicitly expressed in terms of the input data of the problem.

Keywords: multidimensional parabolic equation, inverse problem, Cordes condition, maximum principle, Schauder fixed-point theorem.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation This work was supported by the Program for Enhancing the Competitiveness of Higher-Educational Establishments (NIIYaU MIFI).

DOI: https://doi.org/10.4213/mzm10499

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English version:
Mathematical Notes, 2015, 97:3, 349–361

Bibliographic databases:

Document Type: Article
UDC: 517.95

Citation: V. L. Kamynin, “The Inverse Problem of the Simultaneous Determination of the Right-Hand Side and the Lowest Coefficient in Parabolic Equations with Many Space Variables”, Mat. Zametki, 97:3 (2015), 368–381; Math. Notes, 97:3 (2015), 349–361

Citation in format AMSBIB
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• https://doi.org/10.4213/mzm10499
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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. M. S. Hussein, D. Lesnic, “_orig Simultaneous Determination of Time-Dependent Coefficients and”, Int. J. Comput. Meth. Eng. Sci. Mech., 17:5-6 (2016), 401–411
2. L. Su, P. N. Vabishchevish, V. I. Vasil'ev, “The inverse problem of the simultaneous determination of the right-hand side and the lowest coefficients in parabolic equations”, Numerical Analysis and Its Applications (NAA 2016), Lecture Notes in Computer Science, 10187, eds. I. Dimov, I. Farago, L. Vulkov, Springer, 2017, 633–639
3. 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
4. Huang D., Li Ya., Pei D., “Identification of a Time-Dependent Coefficient in Heat Conduction Problem By New Iteration Method”, Adv. Math. Phys., 2018, 4918256
5. Azizbayov E.I., “The Nonlocal Inverse Problem of the Identification of the Lowest Coefficient and the Right-Hand Side in a Second-Order Parabolic Equation With Integral Conditions”, Bound. Value Probl., 2019, 11
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