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Mat. Zametki, 2013, Volume 94, Issue 2, Pages 207–217 (Mi mz9370)  

This article is cited in 18 scientific papers (total in 18 papers)

The Inverse Problem of Determining the Lower-Order Coefficient in Parabolic Equations with Integral Observation

V. L. Kamynin

National Engineering Physics Institute "MEPhI", Moscow

Abstract: Existence and uniqueness theorems for the solution to the inverse problem of determining the lower-order coefficient in multidimensional parabolic equations with integral observation are obtained. An estimate of the maximum of the modulus of the unknown coefficient with a constant explicitly expressed via the input data of the problem is given.

Keywords: multidimensional parabolic equation, inverse problem for parabolic equations with integral observation, maximum principle, Cordes-type condition.

DOI: https://doi.org/10.4213/mzm9370

Full text: PDF file (542 kB)
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English version:
Mathematical Notes, 2013, 94:2, 205–213

Bibliographic databases:

UDC: 517.95
Received: 26.01.2012

Citation: V. L. Kamynin, “The Inverse Problem of Determining the Lower-Order Coefficient in Parabolic Equations with Integral Observation”, Mat. Zametki, 94:2 (2013), 207–217; Math. Notes, 94:2 (2013), 205–213

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, “The Inverse Problem of the Simultaneous Determination of the Right-Hand Side and the Lowest Coefficient in Parabolic Equations with Many Space Variables”, Math. Notes, 97:3 (2015), 349–361  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. B. Kostin, “Recovery of the coefficient of $u_t$ in the heat equation from a condition of nonlocal observation in time”, Comput. Math. Math. Phys., 55:1 (2015), 85–100  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. A. V. Lakeev, Yu. E. Linke, V. A. Rusanov, “O razreshimosti zadachi realizatsii operator-funktsii nelineinogo regulyatora dinamicheskoi sistemy vtorogo poryadka”, Sib. zhurn. industr. matem., 18:4 (2015), 61–74  mathnet  crossref  mathscinet  elib
    4. M. S. Hussein, D. Lesnic, “Simultaneous determination of time and space-dependent coefficients in a parabolic equation”, Commun. Nonlinear Sci. Numer. Simul., 33 (2016), 194–217  crossref  mathscinet  isi  elib  scopus
    5. L. S. Pulkina, “A problem with dynamic nonlocal condition for pseudohyperbolic equation”, Russian Math. (Iz. VUZ), 60:9 (2016), 38–45  mathnet  crossref  isi
    6. L. S. Pul'kina, A. E. Savenkova, “A problem with a nonlocal with respect to time condition for multidimensional hyperbolic equations”, Russian Math. (Iz. VUZ), 60:10 (2016), 33–43  mathnet  crossref  isi
    7. A. V. Lakeyev, Yu. E. Linke, V. A. Rusanov, “To the structure identification of a nonlinear regulator for a nonstationary hyperbolic system”, Dokl. Math., 93:3 (2016), 339–343  crossref  mathscinet  zmath  isi  elib  scopus
    8. A. B. Kostin, “Inverse problem with nonlocal observation of finding the coefficient multiplying $u_t$ in the parabolic equation”, Differ. Equ., 52:2 (2016), 220–239  crossref  mathscinet  zmath  isi  elib  scopus
    9. A. I. Dreglya, N. A. Sidorov, “Identifikatsiya dinamiki vneshnei sily pri modelirovanii kolebanii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 19 (2017), 105–112  mathnet  crossref
    10. A. B. Beilin, L. S. Pulkina, “Zadacha o kolebaniyakh sterzhnya s neizvestnym usloviem ego zakrepleniya na chasti granitsy”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 2, 7–14  mathnet  elib
    11. Kh. M. Gamzaev, “Chislennyi metod resheniya koeffitsientnoi obratnoi zadachi dlya uravneniya diffuzii–konvektsii–reaktsii”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2017, no. 50, 67–78  mathnet  crossref  elib
    12. 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, ed. Dimov I. Farago I. Vulkov L., Springer International Publishing Ag, 2017, 633–639  crossref  mathscinet  zmath  isi  scopus
    13. A. I. Prilepko, A. B. Kostin, V. V. Solovev, “Obratnye zadachi nakhozhdeniya istochnika i koeffitsientov dlya ellipticheskikh i parabolicheskikh uravnenii v prostranstvakh Geldera i Soboleva”, Sib. zhurn. chist. i prikl. matem., 17:3 (2017), 67–85  mathnet  crossref
    14. A. B. Beilin, “O zadache upravleniya smescheniem odnogo iz kontsov tonkogo sterzhnya”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 3, 12–17  mathnet  crossref  elib
    15. Kh. M. Gamzaev, “Chislennyi metod resheniya koeffitsientnoi obratnoi zadachi dlya nelineinogo uravneniya diffuzii-reaktsii”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 11:1 (2018), 145–151  mathnet  crossref  elib
    16. Kh. M. Gamzaev, S. O. Huseynzade, G. G. Gasimov, “A numerical method to solve identification problem for the lower coefficient and the source in the convection-reaction equation”, Cybern. Syst. Anal., 54:6 (2018), 971–976  crossref  isi  scopus
    17. N. A. Sidorov, A. I. Dreglea, “Integral equations in identification of external force and heat source density dynamics”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, no. 3, 68–77  mathnet
    18. Vabishchevich P.N., “Computational Identification of the Lowest Space-Wise Dependent Coefficient of a Parabolic Equation”, Appl. Math. Model., 65 (2019), 361–376  crossref  mathscinet  isi  scopus
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