V. L. Kamynin, É. Franchini, “An inverse problem for a higher-order parabolic equation”, Mat. Zametki, 64:5 (1998), 680–691; Math. Notes, 64:5 (1998), 590

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Matematicheskie Zametki, 1998, Volume 64, Issue 5, Pages 680–691
DOI: https://doi.org/10.4213/mzm1444 (Mi mzm1444)

This article is cited in 14 scientific papers (total in 14 papers)

An inverse problem for a higher-order parabolic equation

V. L. Kamynin^a, É. Franchini^b

^a Dorodnitsyn Computing Centre of the Russian Academy of Sciences
^b Universita di Milano-Bicocca, Dipartimento di Matematica ed Applicazioni

Full-text PDF (231 kB) Citations (14)

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DOI: https://doi.org/10.4213/mzm1444

Abstract: We prove existence and uniqueness theorems for the inverse problem of finding the right-hand side of a higher-order parabolic equation with two independent variables and an additional condition in the form of integral overdetermination. The results obtained are used to study the passage to the limit in a sequence of such inverse problems with weakly convergent coefficients.

Received: 18.09.1996

English version:
Mathematical Notes, 1998, Volume 64, Issue 5, Pages 590–599
DOI: https://doi.org/10.1007/BF02316283

Bibliographic databases:

UDC: 517.956

Language: Russian

Citation: V. L. Kamynin, É. Franchini, “An inverse problem for a higher-order parabolic equation”, Mat. Zametki, 64:5 (1998), 680–691; Math. Notes, 64:5 (1998), 590–599

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm1444

https://doi.org/10.4213/mzm1444

https://www.mathnet.ru/eng/mzm/v64/i5/p680

This publication is cited in the following 14 articles:

S. G. Pyatkov, “On Some Classes of Inverse Problems on Determining Source Functions for Heat and Mass Transfer Systems”, J Math Sci, 2025
Guzel Ashurova, “Solvability of Coefficient Inverse Problems of Spatial Type for Parabolic Equations with Varying Involution Direction”, J Math Sci, 281:6 (2024), 837
V. L. Kamynin, “Unique Solvability of Direct and Inverse Problems for Degenerate Parabolic Equations in the Multidimensional Case”, J Math Sci, 269:1 (2023), 36
S. G. Pyatkov, “On evolutionary inverse problems for mathematical models of heat and mass transfer”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 14:1 (2021), 5–25
Protsakh N., “Inverse Problem For Higher Order Ultraparabolic Equation With Unknown Minor Coefficient and Right-Hand Side Function”, Miskolc Math. Notes, 21:1 (2020), 335–350
S. G. Pyatkov, “O nekotorykh klassakh obratnykh zadach ob opredelenii funktsii istochnikov dlya sistem teplomassoperenosa”, Differentsialnye uravneniya i matematicheskoe modelirovanie, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 188, VINITI RAN, M., 2020, 23–42
Metin YAMAN, “Long-time Behaviour of Solution to Inverse Problem for Higher-order Parabolic Equation”, Sakarya University Journal of Science, 23:4 (2019), 696
A. I. Kozhanov, “Parabolic equations with unknown time-dependent coefficients”, Comput. Math. Math. Phys., 57:6 (2017), 956–966
V. L. Kamynin, “Inverse problem of determining the right-hand side in a degenerating parabolic equation with unbounded coefficients”, Comput. Math. Math. Phys., 57:5 (2017), 833–842
Kamynin V.L. Bukharova T.I., “Inverse Problems of Determination of the Right-Hand Side Term in the Degenerate Higher-Order Parabolic Equation on a Plane”, 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, 391–397
V. L. Kamynin, “On the Solvability of the Inverse Problem for Determining the Right-Hand Side of a Degenerate Parabolic Equation with Integral Observation”, Math. Notes, 98:5 (2015), 765–777
S. G. Pyatkov, E. I. Safonov, “O nekotorykh klassakh lineinykh obratnykh zadach dlya parabolicheskikh sistem uravnenii”, Sib. elektron. matem. izv., 11 (2014), 777–799
S. G. Pyatkov, E. I. Safonov, “Some inverse problems for convection-diffusion equations”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 7:4 (2014), 36–50
Yaman M., “Blow-Up Solution and Stability to an Inverse Problem for a Pseudo-Parabolic Equation”, J. Inequal. Appl., 2012, 274

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

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