I. A. Kaliev, M. F. Mugafarov, O. V. Fattahova, “Inverse problem for forward-backward parabolic equation with generalized conjugation conditions”, Ufa Math. J., 3:2 (2011), 33

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Ufa Mathematical Journal, 2011, Volume 3, Issue 2, Pages 33–41 (Mi ufa92)

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

Inverse problem for forward-backward parabolic equation with generalized conjugation conditions

I. A. Kaliev^a, M. F. Mugafarov^b, O. V. Fattahova^a

^a Sterlitamak State Pedagogical Academy, Sterlitamak, Russia
^b Ishimbay branch of the Ufa State Aviation Technnical University, Ishimbay, Russia

English version PDF (382 kB) Citations (14) Russian version article

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Abstract: An inverse problem of finding the solution and the right-hand side member of a second order forward-backward parabolic equation with generalized conjugation conditions is considered. Generalized conjugation conditions ensure the symmetry of the problem and provide an opportunity to apply the Hilbert–Schmidt theorem. The system of eigenfunctions is complete and orthogonal. All the eigenvalues of this operator are real and are found by solving a transcendental equation. Using expansion series, we prove the existence and uniqueness of classical solutions of this problem.

Keywords: inverse problem, forward-backward parabolic equation, generalized sewing conditions.

Received: 14.12.2010

Bibliographic databases:

Document Type: Article

UDC: 517.956.4

Language: English

Original paper language: Russian

Citation: I. A. Kaliev, M. F. Mugafarov, O. V. Fattahova, “Inverse problem for forward-backward parabolic equation with generalized conjugation conditions”, Ufa Math. J., 3:2 (2011), 33–41

Citation in format AMSBIB

\Bibitem{KalMugFat11}

\by I.~A.~Kaliev, M.~F.~Mugafarov, O.~V.~Fattahova

\paper Inverse problem for forward-backward parabolic equation with generalized conjugation conditions

\jour Ufa Math. J.

\yr 2011

\vol 3

\issue 2

\pages 33--41

\mathnet{http://mi.mathnet.ru/eng/ufa92}

\zmath{https://zbmath.org/?q=an:1249.35136}

Linking options:

https://www.mathnet.ru/eng/ufa92

https://www.mathnet.ru/eng/ufa/v3/i2/p34

This publication is cited in the following 14 articles:

A. B. Bekiev, “Razreshimost nelokalnoi obratnoi zadachi dlya uravneniya chetvertogo poryadka”, Vestnik KRAUNTs. Fiz.-mat. nauki, 42:1 (2023), 9–26
Roumaissa S., Nadjib B., Faouzia R., “a Variant of Quasi-Reversibility Method For a Class of Heat Equations With Involution Perturbation”, Math. Meth. Appl. Sci., 44:15 (2021), 11933–11943
Turmetov B.Kh., Kadirkulov B.J., “An Inverse Problem For a Parabolic Equation With Involution”, Lobachevskii J. Math., 42:12 (2021), 3006–3015
Mamanazarov A.O., “Unique Solvability of Problems For a Mixed Parabolic Equation in Unbounded Domain”, Lobachevskii J. Math., 41:9, SI (2020), 1837–1845
Kirane M., Sadybekov M.A., Sarsenbi A.A., “on An Inverse Problem of Reconstructing a Subdiffusion Process From Nonlocal Data”, Math. Meth. Appl. Sci., 42:6 (2019), 2043–2052
Bulavatsky V.M., “An Inverse Problem For Anomalous Diffusion Equation With Bi-Ordinal Hilfer'S Derivative”, Cybern. Syst. Anal., 55:2 (2019), 232–239
Al-Salti N., Kirane M., Torebek B.T., “on a Class of Inverse Problems For a Heat Equation With Involution Perturbation”, Hacet. J. Math. Stat., 48:3 (2019), 669–681
M. A. Sadybekov, A. A. Sarsenbi, “On one inverse problem of reconstructing a subdiffusion process with degeneration from nonlocal data”, Doklady AMAN, 19:1 (2019), 31–41
S. G. Pyatkov, E. S. Kvich, “Recovering of lower order coefficients in forward-backward parabolic equations”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 10:4 (2018), 23–29
Erdogan A.S., Kusmangazinova D., Orazov I., Sadybekov M.A., “On One Problem For Restoring the Density of Sources of the Fractional Heat Conductivity Process With Respect to Initial and Final Temperatures”, Bull. Karaganda Univ-Math., 91:3 (2018), 31–44
Aibek B., Aimakhanova A., Besbaev G., Sadybekov M.A., “About One Inverse Problem of Time Fractional Evolution With An Involution Perturbation”, AIP Conference Proceedings, 1997, eds. Ashyralyev A., Lukashov A., Sadybekov M., Amer Inst Physics, 2018, UNSP 020012-1
Sadybekov M.A., Dildabek G., Ivanova M.B., “On An Inverse Problem of Reconstructing a Heat Conduction Process From Nonlocal Data”, Adv. Math. Phys., 2018, 8301656
Ahmad B., Alsaedi A., Kirane M., Tapdigoglu R.G., “An Inverse Problem For Space and Time Fractional Evolution Equations With An Involution Perturbation”, Quaest. Math., 40:2 (2017), 151–160
M. Kirane, N. Al-Salti, “Inverse Problems For a Nonlocal Wave Equation With An Involution Perturbation”, J. Nonlinear Sci. Appl., 9:3 (2016), 1243–1251

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

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Abstract page:	639
Russian version PDF:	232
English version PDF:	37
References:	100
First page:	2

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