|
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.
 Full text:
PDF file (1327 kB)
References:
PDF file
HTML file
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
\Bibitem{PriTik94}
\by A.~I.~Prilepko, I.~V.~Tikhonov
\paper Reconstruction of the nonhomogeneous term in an abstract evolution equation
\jour Izv. RAN. Ser. Mat.
\yr 1994
\vol 58
\issue 2
\pages 167--188
\mathnet{http://mi.mathnet.ru/izv808}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1275907}
\zmath{https://zbmath.org/?q=an:0826.47028}
\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}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RB41200009}
Linking options:
http://mi.mathnet.ru/eng/izv808 http://mi.mathnet.ru/eng/izv/v58/i2/p167
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:
-
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
 -
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
-
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
-
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
 -
A. V. Rozanova, “Controllability for a Nonlinear Abstract Evolution Equation”, Math. Notes, 76:4 (2004), 511–524
-
Prilepko A., Tkachenko D., “Well-Posedness of the Inverse Source Problem for Parabolic Systems”, Differ. Equ., 40:11 (2004), 1619–1626
-
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
-
A. V. Rozanova, “Letter to the Editor”, Math. Notes, 78:5 (2005), 745–745
-
A. I. Kozhanov, “Solvability of the inverse problem of finding thermal conductivity”, Siberian Math. J., 46:5 (2005), 841–856
-
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
-
Lorenzi A., Vrabie I.I., “Identification for a Semilinear Evolution Equation in a Banach Space”, Inverse Probl., 26:8 (2010), 085009
-
Kozhanov A.I., Safiullova R.R., “Linear Inverse Problems for Parabolic and Hyperbolic Equations”, J. Inverse Ill-Posed Probl., 18:1 (2010), 1–24
-
Davide Guidetti, “Determining the Source Term in an Abstract Parabolic Problem From a Time Integral of the Solution”, Mediterr. J. Math, 2011
-
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
-
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
-
A. B. Kostin, “Counterexamples in inverse problems for parabolic, elliptic, and hyperbolic equations”, Comput. Math. Math. Phys., 54:5 (2014), 779–792
-
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
-
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
 -
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
-
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
-
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
-
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
-
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
-
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
-
V. B. Levenshtam, “Parabolic Equations with Large Parameter. Inverse Problems”, Math. Notes, 107:3 (2020), 452–463
|
| Number of views: |
| This page: | 598 | | Full text: | 180 | | References: | 44 | | First page: | 4 |
|
Terms of Use