RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 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

Full text: PDF file (568 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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
\Bibitem{Kam15} \by V.~L.~Kamynin \paper The Inverse Problem of the Simultaneous Determination of the Right-Hand Side and the Lowest Coefficient in Parabolic Equations with Many Space Variables \jour Mat. Zametki \yr 2015 \vol 97 \issue 3 \pages 368--381 \mathnet{http://mi.mathnet.ru/mz10499} \crossref{https://doi.org/10.4213/mzm10499} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3370525} \zmath{https://zbmath.org/?q=an:06455269} \elib{https://elibrary.ru/item.asp?id=23421526} \transl \jour Math. Notes \yr 2015 \vol 97 \issue 3 \pages 349--361 \crossref{https://doi.org/10.1134/S0001434615030062} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000353566800006} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928654716} 

• http://mi.mathnet.ru/eng/mz10499
• https://doi.org/10.4213/mzm10499
• http://mi.mathnet.ru/eng/mz/v97/i3/p368

 SHARE:

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. D. Huang, Ya. Li, D. Pei, “Identification of a time-dependent coefficient in heat conduction problem by new iteration method”, Adv. Math. Phys., 2018, 4918256, 7 pp.
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
6. A. V. Glushak, “Nelokalnaya zadacha dlya abstraktnogo uravneniya Besselya–Struve”, Izv. vuzov. Matem., 2019, no. 7, 29–38
7. V. L. Kamynin, “The Inverse Problem of Simultaneous Determination of the Two Lower Space-Dependent Coefficients in a Parabolic Equation”, Math. Notes, 106:2 (2019), 235–247
8. V. I. Zhegalov, “Ob odnoi zadache dlya obobschennogo uravneniya Bussineska–Lyava”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:4 (2019), 771–776
9. V. L. Kamynin, “The Inverse Problem of Simultaneous Determination of the Two Time-Dependent Lower Coefficients in a Nondivergent Parabolic Equation in the Plane”, Math. Notes, 107:1 (2020), 93–104
10. V. I. Zhegalov, L. B. Mironova, “K zadacham Gursa i Koshi dlya trekhmernogo uravneniya Bianki”, Izv. vuzov. Matem., 2020, no. 6, 15–20
•  Number of views: This page: 307 Full text: 78 References: 60 First page: 69