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Mat. Zametki, 2005, Volume 77, Issue 2, Pages 273–290 (Mi mz2489)  

This article is cited in 10 scientific papers (total in 10 papers)

Uniqueness criterion in an inverse problem for an abstract differential equation with nonstationary inhomogeneous term

I. V. Tikhonova, Yu. S. Èidel'manb

a Moscow Engineering Physics Institute (State University)
b Tel Aviv University

Abstract: In a Banach space $E$, we consider the inverse problem $du(t)/dt=Au(t)+\phi(t)p$, $u(0)=u_0$, $u(T)=u_1$, with an unknown function $u(t)$ and an element $p\in E$. The operator $A$ is assumed linear and closed. In this paper, we establish minimal constraints on the function $\phi\in C([0,T])$ for which the uniqueness of the solution of the inverse problem is completely described in terms of the eigenvalues of the operator $A$.

DOI: https://doi.org/10.4213/mzm2489

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English version:
Mathematical Notes, 2005, 77:2, 246–262

Bibliographic databases:

UDC: 517.95
Received: 19.09.2002

Citation: I. V. Tikhonov, Yu. S. Èidel'man, “Uniqueness criterion in an inverse problem for an abstract differential equation with nonstationary inhomogeneous term”, Mat. Zametki, 77:2 (2005), 273–290; Math. Notes, 77:2 (2005), 246–262

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Glushak, “Inverse problems for evolution equations with fractional integrals at boundary-value conditions”, Journal of Mathematical Sciences, 164:4 (2010), 518–530  mathnet  crossref  mathscinet  elib
    2. A. V. Glushak, “On an Inverse Problem for an Abstract Differential Equation of Fractional Order”, Math. Notes, 87:5 (2010), 654–662  mathnet  crossref  crossref  mathscinet  isi
    3. Popova V.A., Glushak A.V., “Obratnaya zadacha dlya singulyarnogo evolyutsionnogo uravneniya s nelokalnym granichnym usloviem”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2012, no. 1, 182–182  mathscinet  zmath  elib
    4. Ashyralyev A. Erdogan A.S. Demirdag O., “On the Determination of the Right-Hand Side in a Parabolic Equation”, Appl. Numer. Math., 62:11 (2012), 1672–1683  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. 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
    6. I. V. Tikhonov, Yu. V. Gavris, T. Z. Adzhieva, “Struktura reshenii modelnoi obratnoi zadachi teploprovodnosti v klassakh funktsii eksponentsialnogo rosta”, Chelyab. fiz.-matem. zhurn., 1:3 (2016), 37–62  mathnet
    7. 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
    8. 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
    9. S. G. Pyatkov, “On some inverse problems for first order operator-differential equations”, Siberian Math. J., 60:1 (2019), 140–147  mathnet  crossref  crossref  isi  elib
    10. K. B. Sabitov, A. R. Zainullov, “Obratnye zadachi dlya uravneniya teploprovodnosti po otyskaniyu nachalnogo usloviya i pravoi chasti”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 161, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2019, 274–291  mathnet  crossref  elib
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