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Zh. Vychisl. Mat. Mat. Fiz., 2004, Volume 44, Number 4, Pages 694–716 (Mi zvmmf862)  

This article is cited in 57 scientific papers (total in 57 papers)

Nonlinear loaded equations and inverse problems

A. I. Kozhanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

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English version:
Computational Mathematics and Mathematical Physics, 2004, 44:4, 657–675

Bibliographic databases:
UDC: 519.632.8
MSC: Primary 35R30; Secondary 35K25, 35Q53
Received: 16.08.2000
Revised: 02.06.2003

Citation: A. I. Kozhanov, “Nonlinear loaded equations and inverse problems”, Zh. Vychisl. Mat. Mat. Fiz., 44:4 (2004), 694–716; Comput. Math. Math. Phys., 44:4 (2004), 657–675

Citation in format AMSBIB
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\by A.~I.~Kozhanov
\paper Nonlinear loaded equations and inverse problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2004
\vol 44
\issue 4
\pages 694--716
\mathnet{http://mi.mathnet.ru/zvmmf862}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2069212}
\zmath{https://zbmath.org/?q=an:1114.35148}
\transl
\jour Comput. Math. Math. Phys.
\yr 2004
\vol 44
\issue 4
\pages 657--675


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    This publication is cited in the following articles:
    1. A. I. Kozhanov, “Solvability of the inverse problem of finding thermal conductivity”, Siberian Math. J., 46:5 (2005), 841–856  mathnet  crossref  mathscinet  zmath  isi  elib
    2. Kozhanov A.I., “Parabolic equations with an unknown absorption coefficient”, Doklady Mathematics, 74:1 (2006), 573–576  crossref  mathscinet  zmath  isi  elib  scopus
    3. A. I. Kozhanov, “O razreshimosti obratnykh zadach vosstanovleniya koeffitsientov v uravneniyakh sostavnogo tipa”, Vestn. NGU. Ser. matem., mekh., inform., 8:3 (2008), 81–99  mathnet
    4. J. Appl. Industr. Math., 4:3 (2010), 332–339  mathnet  crossref  mathscinet
    5. A. I. Kozhanov, “On the Solvability of Boundary Value Problems for the Quasilinear Ultraparabolic Equations of Certain Mathematical Models of the Dynamics of Biological Systems”, J. Appl. Industr. Math., 4:4 (2010), 512–525  mathnet  crossref  mathscinet
    6. E. P. Melisheva, “Zadacha Dirikhle dlya nagruzhennogo uravneniya Lavrenteva–Bitsadze”, Vestn. SamGU. Estestvennonauchn. ser., 2010, no. 6(80), 39–47  mathnet
    7. 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  mathnet  zmath
    8. Kozhanov A.I., “Parabolicheskie uravneniya s neizvestnym koeffitsientom pogloscheniya”, Vestnik Chelyabinskogo gosudarstvennogo universiteta, 2011, no. 26, 5–19  mathscinet  elib
    9. Telesheva L.A., “O razreshimosti obratnoi zadachi dlya parabolicheskogo uravneniya vysokogo poryadka s neizvestnym koeffitsientom pri proizvodnoi po vremeni”, Matematicheskie zametki YaGU, 18:2 (2011), 180–201  zmath  elib
    10. Kozhanov A.I., “O razreshimosti nekotorykh nelokalnykh i svyazannykh s nimi obratnykh zadach dlya parabolicheskikh uravnenii”, Matematicheskie zametki YaGU, 18:2 (2011), 64–78  mathscinet  zmath  elib
    11. Kosheleva Yu.A., “O razreshimosti nekotorykh lineinykh obratnykh zadach dlya ultraparabolicheskikh uravnenii”, Matematicheskie zametki YaGU, 18:2 (2011), 79–98  mathscinet  zmath  elib
    12. A. I. Kozhanov, “Parabolicheskie uravneniya s neizvestnym koeffitsientom pogloscheniya”, Vestnik ChelGU, 2011, no. 13, 5–19  mathnet
    13. I. Orazov, M. A. Sadybekov, “One nonlocal problem of determination of the temperature and density of heat sources”, Russian Math. (Iz. VUZ), 56:2 (2012), 60–64  mathnet  crossref  mathscinet
    14. I. Orazov, M. A. Sadybekov, “On a class of problems of determining the temperature and density of heat sources given initial and final temperature”, Siberian Math. J., 53:1 (2012), 146–151  mathnet  crossref  mathscinet  isi
    15. K. B. Sabitov, N. V. Martem'yanova, “An inverse problem for an equation of elliptic-hyperbolic type with a nonlocal boundary condition”, Siberian Math. J., 53:3 (2012), 507–519  mathnet  crossref  mathscinet  isi
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    19. A. I. Kozhanov, “Lineinye obratnye zadachi dlya odnogo klassa vyrozhdayuschikhsya uravnenii sobolevskogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 11, 33–42  mathnet
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    22. S. G. Pyatkov, A. G. Borichevskaya, “O nekotorykh obratnykh zadachakh dlya matematicheskikh modelei teplomassoperenosa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 6:4 (2013), 63–72  mathnet
    23. R. R. Safiullova, “Obratnaya zadacha dlya giperbolicheskogo uravneniya vtorogo poryadka s neizvestnym koeffitsientom, zavisyaschim ot vremeni”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 6:4 (2013), 73–86  mathnet
    24. E. P. Melisheva, “Zadacha Dirikhle dlya nagruzhennogo vyrozhdayuschegosya uravneniya smeshannogo tipa v pryamougolnoi oblasti”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 6(107), 40–53  mathnet
    25. Yuriy Ya. Belov, Kirill V. Korshun, “On solvability of the Cauchy problem for a loaded system”, Zhurn. SFU. Ser. Matem. i fiz., 7:2 (2014), 155–161  mathnet
    26. Orazov I., Makhatova A., “An Inverse Problem of Mathematical Modeling of the Extraction Process of Polydisperse Porous Materials”, International Conference on Analysis and Applied Mathematics, AIP Conference Proceedings, 1611, eds. Ashyralyev A., Malkowsky E., Amer Inst Physics, 2014, 225–230  crossref  adsnasa  isi  scopus
    27. E. N. Kriger, I. V. Frolenkov, “An identification problem of coefficient in the special form at nonlinear lowest term for two-dimensional semilinear parabolic equation with the Cauchy data”, Russian Math. (Iz. VUZ), 59:5 (2015), 17–31  mathnet  crossref
    28. L. I. Kononenko, “Pryamaya i obratnaya zadachi dlya singulyarnoi sistemy s medlennymi i bystrymi peremennymi v khimicheskoi kinetike”, Vladikavk. matem. zhurn., 17:1 (2015), 39–46  mathnet
    29. K. B. Sabitov, “Initial-boundary problem for parabolic-hyperbolic equation with loaded summands”, Russian Math. (Iz. VUZ), 59:6 (2015), 23–33  mathnet  crossref
    30. Amangaliyeva M.M., Jenaliyev M.T., Kosmakova M.T., Ramazanov M.I., “Uniqueness and Non-Uniqueness of Solutions of the Boundary Value Problems of the Heat Equation”, Advancements in Mathematical Sciences (Ams 2015), AIP Conference Proceedings, 1676, eds. Ashyralyev A., Malkowsky E., Lukashov A., Basar F., Amer Inst Physics, 2015, 020028  crossref  isi
    31. V. M. Abdullayev, K. R. Aida-zade, “Finite-difference methods for solving loaded parabolic equations”, Comput. Math. Math. Phys., 56:1 (2016), 93–105  mathnet  crossref  crossref  isi  elib
    32. E. A. Utkina, “O zadachakh so smescheniyami v granichnykh usloviyakh dlya giperbolicheskogo uravneniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:1 (2016), 65–73  mathnet  crossref  zmath  elib
    33. Ekaterina N. Kriger, Igor V. Frolenkov, “An identification problem of nonlinear lowest term coefficient in the special form for two-dimensional semilinear parabolic equation”, Zhurn. SFU. Ser. Matem. i fiz., 9:2 (2016), 180–191  mathnet  crossref
    34. S. Z. Djamalov, “The linear inverse problem for the equation of Trikomi in three-dimensional space”, Bulletin KRASEC. Phys. & Math. Sci., 13:2 (2016), 10–15  mathnet  crossref  crossref  mathscinet  elib
    35. Yu. Ya. Belov, K. V. Korshun, “On solvability of some parametric inverse problem for parabolic equation”, J. Math. Sci., 228:4 (2018), 347–356  mathnet  crossref  crossref
    36. R. R. Safiullova, “On a solvability of the nonlinear inverse problem for the hyperbolic equation”, J. Math. Sci., 228:4 (2018), 431–448  mathnet  crossref  crossref
    37. S. G. Pyatkov, S. N. Shergin, “Inverse problems for some Sobolev-type mathematical models”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:2 (2016), 75–89  mathnet  crossref  elib
    38. Aida-zade K.R. Abdullayev V.M., “Solution To a Class of Inverse Problems For a System of Loaded Ordinary Differential Equations With Integral Conditions”, J. Inverse Ill-Posed Probl., 24:5 (2016), 543–558  crossref  mathscinet  zmath  isi  elib
    39. A. I. Kozhanov, “Obratnye zadachi vosstanovleniya pravoi chasti spetsialnogo vida v parabolicheskom uravnenii”, Matematicheskie zametki SVFU, 23:4 (2016), 31–45  mathnet  elib
    40. Yu. A. Kosheleva, “O razreshimosti nekotorykh nelineinykh obratnykh zadach dlya ultraparabolicheskikh uravnenii”, Sib. elektron. matem. izv., 13 (2016), 1187–1206  mathnet  crossref
    41. S. Z. Dzhamalov, “Lineinaya obratnaya zadacha dlya uravneniya smeshannogo tipa vtorogo roda vtorogo poryadka s nelokalnymi granichnymi usloviyami v trekhmernom prostranstve”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2017, no. 1(17), 7–13  mathnet  crossref  mathscinet  elib
    42. V. M. Abdullayev, K. R. Aida-zade, “Optimization of loading places and load response functions for stationary systems”, Comput. Math. Math. Phys., 57:4 (2017), 634–644  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    43. V. R. Barsegyan, “Zadacha upravleniya dlya odnoi sistemy lineinykh nagruzhennykh differentsialnykh uravnenii s nerazdelennymi mnogotochechnymi promezhutochnymi usloviyami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 21 (2017), 19–32  mathnet  crossref
    44. Nikolaev N.N., Popov S.V., “On the Problem of Recovering the Coefficients in a One-Dimensional Third Order Equation”, Proceedings of the 8th International Conference on Mathematical Modeling (ICMM-2017), AIP Conference Proceedings, 1907, eds. Egorov I., Popov S., Vabishchevich P., Antonov M., Lazarev N., Troeva M., Troeva M., Ivanova A., Gri, Amer Inst Physics, 2017, UNSP 030005  crossref  isi  scopus
    45. Azizbayov E., Mehraliyev Ya., “Inverse Problem For a Parabolic Equation in a Rectangle Domain With Integral Conditions”, Eur. J. Pure Appl Math., 10:5 (2017), 981–994  mathscinet  zmath  isi
    46. Abdullayev V.M., “Identification of the Functions of Response to Loading For Stationary Systems”, Cybern. Syst. Anal., 53:3 (2017), 417–425  crossref  mathscinet  zmath  isi  scopus
    47. 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  mathnet  crossref
    48. Baltaeva U.I., “On the Solvability of Boundary-Value Problems With Continuous and Generalized Gluing Conditions For the Equation of Mixed Type With Loaded Term”, Ukr. Math. J., 69:12 (2018), 1845–1854  crossref  mathscinet  isi  scopus
    49. V. R. Barseghyan, “The control problem for stage-by-stage changing linear systems of loaded differential equations”, Autom. Remote Control, 79:4 (2018), 594–603  mathnet  crossref  isi  elib
    50. Barseghyan V.R., Barseghyan T.V., 5Th International Conference on Topical Problems of Continuum Mechanics With a Special Session in Honor of Alexander Manzhirov'S 60Th Birthday, Journal of Physics Conference Series, 991, IOP Publishing Ltd, 2018  crossref  isi  scopus
    51. S. Z. Dzhamalov, “Ob odnoi obratnoi zadache dlya mnogomernogo uravneniya smeshannogo tipa pervogo roda, vtorogo poryadka s periodicheskimi usloviyami”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2018, no. 4(24), 10–18  mathnet  crossref  elib
    52. V. R. Barsegyan, T. A. Simonyan, T. V. Barsegyan, “O zadache optimalnoi stabilizatsii odnoi sistemy lineinykh nagruzhennykh differentsialnykh uravnenii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 27 (2019), 71–79  mathnet  crossref
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