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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, Number 6, Pages 11–22
DOI: https://doi.org/10.26907/0021-3446-2019-6-11-22 (Mi ivm9469) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On one linear inverse problem for multidimensional equation of the mixed type of the first kind and of the second order

S. Z. Djamalovab, R. R. Ashurovac

a Institute of Mathematics, Uzbekistan Academy of Sciences, 81 Mirzo Ulugbek str., Akademgorodok, Tashkent, 100170 Republic of Uzbekistan
b Gubkin Russian State University of Oil and Gas of Tashkent, 34 Durmon yuli str., Tashkent, 100125 Republic of Uzbekistan
c National University of Uzbekistan named aftar M. Ulugbek, 4 University str., Tashkent, 100174 Republic of Uzbekistan
Full-text PDF (379 kB) Citations (12)
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DOI: https://doi.org/10.26907/0021-3446-2019-6-11-22
Abstract: In the present work we consider the problems of correctness of a linear inverse problem for the multidimensional equation of the mixed type of the first kind and of the second order. For this problem, the theorems on existence and uniqueness of the solution are proved in a certain class by "ε-regularization", a priori estimations and of successive approximations methods.
Keywords: multidimensional equation of mixed type of first kind, second order, linear inverse problem, correctness of solution, "ε-regularization", a priori estimation successive approximation method.
Received: 10.05.2018
Revised: 10.05.2018
Accepted: 26.09.2018
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, Volume 63, Issue 6, Pages 8–18
DOI: https://doi.org/10.3103/S1066369X19060021
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: S. Z. Djamalov, R. R. Ashurov, “On one linear inverse problem for multidimensional equation of the mixed type of the first kind and of the second order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 6, 11–22; Russian Math. (Iz. VUZ), 63:6 (2019), 8–18
Citation in format AMSBIB
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\issue 6
\pages 11--22
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\vol 63
\issue 6
\pages 8--18
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  • https://www.mathnet.ru/eng/ivm9469
  • https://www.mathnet.ru/eng/ivm/y2019/i6/p11
    • This publication is cited in the following 12 articles:
    1. S. Z. Djamalov, B. K. Sipatdinova, “A linear inverse problem for a three-dimensional mixed-type equation of the second kind, second order with semi-nonlocal boundary condition in an unbounded parallelepiped”, Chelyab. fiz.-matem. zhurn., 9:3 (2024), 471–482  mathnet  crossref
    2. R. R. Ashurov, M. B. Murzambetova, “Inverse Problem for Mixed-type Equation with an Elliptic Operator of Arbitrary Order”, Lobachevskii J Math, 44:2 (2023), 533  crossref
    3. O. Kh. Abdullaev, T. K. Yuldashev, “Inverse Problems for the Loaded Parabolic-Hyperbolic Equation Involves Riemann–Liouville Operator”, Lobachevskii J Math, 44:3 (2023), 1080  crossref
    4. A. K. Fayziyev, A. N. Abdullozhonova, T. K. Yuldashev, “Inverse Problem for Whitham Type Multi-Dimensional Differential Equation with Impulse Effects”, Lobachevskii J Math, 44:2 (2023), 570  crossref
    5. Sirojiddin Z. Dzhamalov, Ravshan Ashurov, Alexandr Kozhanov, “Linear Inverse Problem for 3-Dimensional Chaplygin Equation with Semi–Nonlocal Boundary Conditions in a Prismatic Unbounded Domain”, J Math Sci, 274:2 (2023), 186  crossref
    6. R. R. Ashurov, M. B. Murzambetova, “Kraevaya zadacha dlya uravneniya smeshannogo tipa s ellipticheskim operatorom vysokogo poryadka”, Vestnik KRAUNTs. Fiz.-mat. nauki, 39:2 (2022), 7–19  mathnet  crossref  mathscinet
    7. T. K. Yuldashev, O. Sh. Kilichev, “Nonlinear Inverse Problem for a Sixth Order Differential Equation with Two Redefinition Functions”, Lobachevskii J Math, 43:3 (2022), 804  crossref
    8. T. K. Yuldashev, A. K. Fayziyev, “Integral Condition with Nonlinear Kernel for an Impulsive System of Differential Equations with Maxima and Redefinition Vector”, Lobachevskii J Math, 43:8 (2022), 2332  crossref
    9. R. R. Ashurov, R. T. Zunnunov, “Inverse problem for determining the order of the fractional derivative in mixed-type equations”, Lobachevskii J. Math., 42:12 (2021), 2714–2729  crossref  mathscinet  isi  scopus
    10. S. Z. Dzhamalov, R. R. Ashurov, U. Sh. Ruziev, “On a seminonlocal boundary value problem for a multidimensional loaded mixed type equation of the second kind”, Lobachevskii J. Math., 42:3, SI (2021), 536–543  crossref  mathscinet  isi  scopus
    11. S. Z. Dzhamalov, R. R. Ashurov, Kh. Sh. Turakulov, “The Linear Inverse Problem for the Three-Dimensional Tricomi Equation in a Prismatic Unbounded Domain”, Lobachevskii J Math, 42:15 (2021), 3606  crossref
    12. S. Z. Dzhamalov, S. R. Umarov, R. R. Ashurov, “On unique solvability of a nonlocal boundary-value problem for a loaded multidimensional Chaplygin's equation in the Sobolev space”, Lobachevskii J. Math., 41:1, SI (2020), 7–14  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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