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

This article is cited in 5 scientific papers (total in 5 papers)

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
Received: 09.04.2014

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

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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  crossref  mathscinet  isi  elib  scopus
    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  crossref  mathscinet  zmath  isi  scopus
    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  mathnet  crossref  elib
    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  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  isi  scopus
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