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Izv. RAN. Ser. Mat., 1994, Volume 58, Issue 2, Pages 167–188 (Mi izv808)  

This article is cited in 25 scientific papers (total in 25 papers)

Reconstruction of the nonhomogeneous term in an abstract evolution equation

A. I. Prilepko, I. V. Tikhonov


Abstract: A nonhomogeneous evolution equation the right-hand side of which is unknown is considered in a Banach space. For the determination of the unknown right-hand side, in addition to the Cauchy condition, a special overdetermination is given. In the paper a systematic theory for the investigation of the problem indicated is constructed, and sufficient conditions for the existence and uniqueness of solution are given. Special attention is paid to certain problems of perturbation theory.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1995, 44:2, 373–394

Bibliographic databases:

UDC: 517.9
MSC: 47D06
Received: 18.03.1992

Citation: A. I. Prilepko, I. V. Tikhonov, “Reconstruction of the nonhomogeneous term in an abstract evolution equation”, Izv. RAN. Ser. Mat., 58:2 (1994), 167–188; Russian Acad. Sci. Izv. Math., 44:2 (1995), 373–394

Citation in format AMSBIB
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\by A.~I.~Prilepko, I.~V.~Tikhonov
\paper Reconstruction of the nonhomogeneous term in an abstract evolution equation
\jour Izv. RAN. Ser. Mat.
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\vol 58
\issue 2
\pages 167--188
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1995IzMat..44..373P}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1995
\vol 44
\issue 2
\pages 373--394
\crossref{https://doi.org/10.1070/IM1995v044n02ABEH001602}
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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. Tikhonov I., “Solvability of a Problem with a Nonlocal Integral Condition for a Differential Equation in a Banach Space”, Differ. Equ., 34:6 (1998), 841–844  mathnet  mathscinet  zmath  isi
    2. Prilepko A., Tikhonov I., “A Positive Solution Principle for a Linear Inverse Problem and Applications to a Coefficient Problem of Heat Conductivity”, Dokl. Akad. Nauk, 364:1 (1999), 21–23  mathnet  mathscinet  zmath  isi
    3. A. I. Prilepko, D. S. Tkachenko, “The Fredholm property and the well-posedness of the inverse source problem with integral overdetermination”, Comput. Math. Math. Phys., 43:9 (2003), 1338–1347  mathnet  mathscinet  zmath
    4. A. I. Prilepko, D. S. Tkachenko, “Properties of solutions of a parabolic equation and the uniqueness of the solution of the inverse source problem with integral overdetermination”, Comput. Math. Math. Phys., 43:4 (2003), 537–546  mathnet  mathscinet  zmath  elib
    5. A. V. Rozanova, “Controllability for a Nonlinear Abstract Evolution Equation”, Math. Notes, 76:4 (2004), 511–524  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Prilepko A., Tkachenko D., “Well-Posedness of the Inverse Source Problem for Parabolic Systems”, Differ. Equ., 40:11 (2004), 1619–1626  mathnet  crossref  mathscinet  zmath  isi
    7. V. L. Kamynin, “On the inverse problem of determining the right-hand side of a parabolic equation under an integral overdetermination condition”, Math. Notes, 77:4 (2005), 482–493  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. A. V. Rozanova, “Letter to the Editor”, Math. Notes, 78:5 (2005), 745–745  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    9. A. I. Kozhanov, “Solvability of the inverse problem of finding thermal conductivity”, Siberian Math. J., 46:5 (2005), 841–856  mathnet  crossref  mathscinet  zmath  isi  elib
    10. Prilepko A.I., “The semigroup method for inverse, nonlocal, and nonclassical problems. Prediction-control and prediction-observation for evolution equations: I”, Differential Equations, 41:11 (2005), 1635–1646  mathnet  crossref  mathscinet  zmath  isi  elib
    11. Lorenzi A., Vrabie I.I., “Identification for a Semilinear Evolution Equation in a Banach Space”, Inverse Probl., 26:8 (2010), 085009  crossref  mathscinet  zmath  adsnasa  isi
    12. Kozhanov A.I., Safiullova R.R., “Linear Inverse Problems for Parabolic and Hyperbolic Equations”, J. Inverse Ill-Posed Probl., 18:1 (2010), 1–24  crossref  mathscinet  isi
    13. Davide Guidetti, “Determining the Source Term in an Abstract Parabolic Problem From a Time Integral of the Solution”, Mediterr. J. Math, 2011  crossref
    14. Kamynin V.L., Bukharova T.I., “Obratnaya zadacha opredeleniya funktsii istochnika v nedivergentnom parabolicheskom uravnenii”, Vestnik rossiiskogo universiteta druzhby narodov. seriya: matematika, informatika, fizika, 2012, no. 3, 5–12  elib
    15. A. B. Kostin, “The inverse problem of recovering the source in a parabolic equation under a condition of nonlocal observation”, Sb. Math., 204:10 (2013), 1391–1434  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. A. B. Kostin, “Counterexamples in inverse problems for parabolic, elliptic, and hyperbolic equations”, Comput. Math. Math. Phys., 54:5 (2014), 779–792  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    17. 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
    18. Kostin A.B., “Inverse problem of finding the coefficient of u in a parabolic equation on the basis of a nonlocal observation condition”, Differ. Equ., 51:5 (2015), 605–619  crossref  mathscinet  zmath  isi  elib  scopus
    19. T. K. Yuldashev, “Obratnaya zadacha dlya obyknovennogo integro-differentsialnogo uravneniya s vyrozhdennym yadrom i nelokalnymi integralnymi usloviyami”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2016, no. 3, 19–33  mathnet  crossref  elib
    20. Kostin A.B., “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
    21. A. V. Karev, I. V. Tikhonov, “Raspredelenie nulei odnoi tseloi funktsii tipa Mittag-Lefflera s prilozheniyami v teorii obratnykh zadach”, Chelyab. fiz.-matem. zhurn., 2:4 (2017), 430–446  mathnet  elib
    22. Yuldashev T.K., “Determination of the Coefficient and Boundary Regime in Boundary Value Problem For Integro-Differential Equation With Degenerate Kernel”, Lobachevskii J. Math., 38:3, SI (2017), 547–553  crossref  isi
    23. 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
    24. Vu Nguen Shon Tung, “Spetsialnye primery superustoichivykh polugrupp i ikh primenenie v teorii obratnykh zadach”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:3 (2018), 252–262  mathnet  crossref  elib
    25. V. B. Levenshtam, “Parabolic Equations with Large Parameter. Inverse Problems”, Math. Notes, 107:3 (2020), 452–463  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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