Abstract:
Uniqueness and existence theorems for the solution of the inverse problem for a degenerating parabolic equation with unbounded coefficients on a plane in conditions of integral observations are proven. Estimates of the solution with constants explicitly expresses via the input data of the problem are obtained.
Key words:
inverse problems, condition of integral observation, degenerating parabolic equations, unbounded coefficients of equation.
Citation:
V. L. Kamynin, “Inverse problem of determining the right-hand side in a degenerating parabolic equation with unbounded coefficients”, Zh. Vychisl. Mat. Mat. Fiz., 57:5 (2017), 832–841; Comput. Math. Math. Phys., 57:5 (2017), 833–842
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\by V.~L.~Kamynin
\paper Inverse problem of determining the right-hand side in a degenerating parabolic equation with unbounded coefficients
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2017
\vol 57
\issue 5
\pages 832--841
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\jour Comput. Math. Math. Phys.
\yr 2017
\vol 57
\issue 5
\pages 833--842
\crossref{https://doi.org/10.1134/S0965542517050049}
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Linking options:
https://www.mathnet.ru/eng/zvmmf10573
https://www.mathnet.ru/eng/zvmmf/v57/i5/p832
This publication is cited in the following 18 articles:
Gulaiym Oralsyn, Trends in Mathematics, 5, Women in Analysis and PDE, 2024, 293
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
V. L. Kamynin, “Inverse Problems of Finding the Lower Term in a Multidimensional Degenerate Parabolic Equation”, J Math Sci, 274:4 (2023), 493
V. L. Kamynin, “Ob obratnoi zadache opredeleniya zavisyaschego ot prostranstvennoi peremennoi mladshego koeffitsienta v parabolicheskom uravnenii so slabym vyrozhdeniem”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 28 yanvarya – 2 fevralya 2021 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 206, VINITI RAN, M., 2022, 68–81
V. L. Kamynin, “The Inverse Problem of Recovering the Source Function in a Multidimensional Nonuniformly Parabolic Equation”, Math. Notes, 112:3 (2022), 412–423
A. Samreen, S. A. Malik, “An inverse problem for a multi-term fractional differential equation with two-parameter fractional derivatives in time and Bessel operator”, Math. Meth. Appl. Sci., 44:11 (2021), 9541–9556
V. L. Kamynin, “Inverse problem of determining the absorption coefficient in a degenerate parabolic equation in the class $L_\infty$”, Comput. Math. Math. Phys., 61:3 (2021), 388–402
N. V. Martemyanova, “Nonlocal inverse problem to find unknown multipliers in right part of Lavrentev–Bitsadze equation”, Russian Math. (Iz. VUZ), 64:1 (2020), 40–57
M. S. Hussein, D. Lesnic, V. L. Kamynin, A. B. Kostin, “Direct and inverse source problems for degenerate parabolic equations”, J. Inverse Ill-Posed Probl., 28:3 (2020), 425–448
M. J. Huntul, D. Lesnic, “Determination of time-dependent coefficients for a weakly degenerate heat equation”, CMES-Comp. Model. Eng. Sci., 123:2 (2020), 475–494
V. L. Kamynin, “Inverse Problem of Determining the Absorption Coefficient in a Degenerate Parabolic Equation in the Class of L2-Functions”, J Math Sci, 250:2 (2020), 322
V. Kamynin, A. B. Kostin, “Determination of the right-hand side term in the degenerate parabolic equation with two variables”, VII International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 1205, IOP Publishing Ltd, 2019, 012023
E. I. Azizbayov, Ya. T. Mehraliyev, “Nonlocal inverse problem for determination of time derivative coefficient in a second-order parabolic equation”, Adv. Differ. Equ. Control Process., 19:1 (2018), 15–36
V. L. Kamynin, “Asymptotic behavior of solutions of inverse problems for degenerate parabolic equations”, Differ. Equ., 54:5 (2018), 633–647
A. I. Prilepko, V. L. Kamynin, A. B. Kostin, “Inverse source problem for parabolic equation with the condition of integral observation in time”, J. Inverse Ill-Posed Probl., 26:4 (2018), 523–539
V. L. Kamynin, “On inverse problems for strongly degenerate parabolic equations under the integral observation condition”, Comput. Math. Math. Phys., 58:12 (2018), 2002–2017
V. L. Kamynin, “On the Stabilization to Zero of the Solutions of the Inverse Problem for a Degenerate Parabolic Equation with Two Independent Variables”, Math. Notes, 101:6 (2017), 974–983
Kamynin V.L., Bukharova T.I., Vi International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 937, IOP Publishing Ltd, 2017
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