V. L. Kamynin, “On the Unique Solvability of an Inverse Problem for Parabolic Equations under a Final Overdetermination Condition”, Mat. Zametki, 73:2 (2003), 217–227; Math. Notes, 73:2 (2003), 202

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Matematicheskie Zametki, 2003, Volume 73, Issue 2, Pages 217–227
DOI: https://doi.org/10.4213/mzm180 (Mi mzm180)

This article is cited in 34 scientific papers (total in 34 papers)

On the Unique Solvability of an Inverse Problem for Parabolic Equations under a Final Overdetermination Condition

V. L. Kamynin

Moscow Engineering Physics Institute (State University)

Full-text PDF (209 kB) Citations (34)

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DOI: https://doi.org/10.4213/mzm180

Abstract: We consider the unique solvability of the inverse problem of determining the right-hand side of a parabolic equation with the leading coefficient depending on time and space variables under a final overdetermination condition. We obtain two types of conditions that are sufficient for the local solvability of the inverse problem and also prove the so-called Fredholm solvability of the inverse problem under study.

Received: 06.08.2001

English version:
Mathematical Notes, 2003, Volume 73, Issue 2, Pages 202–211
DOI: https://doi.org/10.1023/A:1022107024916

Bibliographic databases:

UDC: 517.956

Language: Russian

Citation: V. L. Kamynin, “On the Unique Solvability of an Inverse Problem for Parabolic Equations under a Final Overdetermination Condition”, Mat. Zametki, 73:2 (2003), 217–227; Math. Notes, 73:2 (2003), 202–211

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm180

https://doi.org/10.4213/mzm180

https://www.mathnet.ru/eng/mzm/v73/i2/p217

This publication is cited in the following 34 articles:

J. Sh. Safarov, U. N. Kalandarov, M. J. Safarova, “Inverse Problem of Determining a Kernel of the Viscoelasticity Equation with Distributed Data in a Limited Domain”, Lobachevskii J Math, 45:7 (2024), 3380
D. A. Tursunov, K. G. Kozhobekov, A. O. Mamytov, B. E. Matieva, “Solvability of One Class of Inverse Problem for Partial Differential Equations”, Lobachevskii J Math, 45:7 (2024), 3453
V. L. Kamynin, “OB OBRATNOI ZADAChE OPREDELENIYa KOEFFITsIENTA POGLOSchENIYa V PARABOLIChESKOM URAVNENII PRI USLOVII FINALNOGO NABLYuDENIYa”, Vestnik, 13:5 (2024), 329
D. A. Tursunov, K. G. Kozhobekov, A. O. Mamytov, E. A. Tursunov, “The Inverse Problem of Recovering the Kernel and the Right-Hand Side of a Fifth Order Integro-Differential Equation”, Lobachevskii J Math, 45:10 (2024), 5295
B. C. Ablabekov, A. B. Ablabekova, “Inverse Problem of Determining the Source in the Aller–Lykov Equation with a Final Redefinition”, Lobachevskii J Math, 44:7 (2023), 2542
Miglena N. Koleva, Lubin G. Vulkov, “Reconstruction coefficient analysis of honeybee collapse due to pesticide contamination”, J. Phys.: Conf. Ser., 2675:1 (2023), 012024
Huntul M.J. Oussaeif T.-E., “Solvability of the Nonlocal Inverse Parabolic Problem and Numerical Results”, Comput. Syst. Sci. Eng., 40:3 (2022), 1109–1126
Kai Cao, “Determination of the Space-Dependent Source Term in a Fourth-Order Parabolic Problem”, Appl Math Optim, 86:2 (2022)
Vladimir Romanov, Alemdar Hasanov, “Uniqueness and stability analysis of final data inverse source problems for evolution equations”, Journal of Inverse and Ill-posed Problems, 30:3 (2022), 425
Shahsahebi F.S., Damirchi J., Janmohammadi A., “The Ritz-Galerkin Procedure For An Inverse Space-Dependent Heat Source Problem”, Jpn. J. Ind. Appl. Math., 38:2 (2021), 625–643
T. K. Yuldashev, “Obratnaya smeshannaya zadacha dlya integro-differentsialnogo uravneniya s mnogomernym operatorom Benni—Lyuka i nelineinymi maksimumami”, Differentsialnye uravneniya, geometriya i topologiya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 201, VINITI RAN, M., 2021, 3–15
Phan Xuan Thanh, “Space-Time Finite Element Method For Determination of a Source in Parabolic Equations From Boundary Observations”, J. Inverse Ill-Posed Probl., 29:5 (2021), 689–705
Hasanov A., Romanov V., Baysal O., “Unique Recovery of Unknown Spatial Load in Damped Euler-Bernoulli Beam Equation From Final Time Measured Output”, Inverse Probl., 37:7 (2021), 075005
LingDe Su, V. I. Vasil'ev, “Identification of spacewise dependent right-hand side in two dimensional parabolic equation”, J. Phys.: Conf. Ser., 2092:1 (2021), 012019
Anjuna Dileep, Alemdar Hasanov, Kumarasamy Sakthivel, Cristiana Sebu, “On unique determination of an unknown spatial load in damped Euler–Bernoulli beam equation from final time output”, Journal of Inverse and Ill-posed Problems, 2021
Sazaklioglu A.U., Erdogan A.S., Ashyralyev A., “Existence and Uniqueness Results For An Inverse Problem For a Semilinear Equation With Final Overdetermination”, Filomat, 32:3 (2018), 847–858
Sazaklioglu A.U., Ashyralyev A., Erdogan A.S., “Existence and Uniqueness Results For An Inverse Problem For Semilinear Parabolic Equations”, Filomat, 31:4 (2017), 1057–1064
Dinh Nho Hao Bui Viet Huong Nguyen Thi Ngoc Oanh Phan Xuan Thanh, “Determination of a term in the right-hand side of parabolic equations”, J. Comput. Appl. Math., 309 (2017), 28–43
Ashyralyev A., Sazaklioglu A.U., “Investigation of a Time-Dependent Source Identification Inverse Problem With Integral Overdetermination”, Numer. Funct. Anal. Optim., 38:10 (2017), 1276–1294
Shidfar A., Darooghehgimofrad Z., “A Numerical Algorithm Based on Rbfs For Solving An Inverse Source Problem”, Bull. Malays. Math. Sci. Soc., 40:3 (2017), 1149–1158

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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