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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 156, Pages 106–116 (Mi into402)  
This article is cited in 7 scientific papers (total in 7 papers)

Initial-value problem for a higher-order partial quasilinear differential equation

T. K. Yuldasheva, K. H. Shabadikovb

a M. F. Reshetnev Siberian State University of Science and Technologies
b Ferghana State University
Full-text PDF (184 kB) Citations (7)
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Abstract: We examine an initial-value problem for a certain higher-order partial quasilinear differential equation. Expressing the partial differential operator as the superposition of first-order operator, we apply methods of solution of first-order equations. We prove the unique solvability of the initial-value problem considered.
Keywords: initial-value problem, characteristics, directional derivative, superposition of differential operators, unique solvability.
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 254, Issue 6, Pages 811–822
DOI: https://doi.org/10.1007/s10958-021-05343-0
Bibliographic databases:
Document Type: Article
UDC: 517.955.2
MSC: 35A30, 35C15, 35G55, 35L30
Language: Russian
Citation: T. K. Yuldashev, K. H. Shabadikov, “Initial-value problem for a higher-order partial quasilinear differential equation”, Mathematical Analysis, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 156, VINITI, Moscow, 2018, 106–116; J. Math. Sci. (N. Y.), 254:6 (2021), 811–822
Citation in format AMSBIB
\Bibitem{YulSha18}
\by T.~K.~Yuldashev, K.~H.~Shabadikov
\paper Initial-value problem for a higher-order partial quasilinear differential equation
\inbook Mathematical Analysis
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 156
\pages 106--116
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into402}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3939201}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 254
\issue 6
\pages 811--822
\crossref{https://doi.org/10.1007/s10958-021-05343-0}
Linking options:
  • https://www.mathnet.ru/eng/into402
  • https://www.mathnet.ru/eng/into/v156/p106
    • This publication is cited in the following 7 articles:
    1. Tursun K. Yuldashev, Najmiddin N. Qodirov, Mansur P. Eshov, Gulnora K. Abdurakhmanova, IUTAM Bookseries, 40, Proceedings of the IUTAM Symposium on Optimal Guidance and Control for Autonomous Systems 2023, 2024, 205  crossref
    2. T. K. Yuldashev, M. M. Babayev, “On Solvability of a Mixed Problem for a Fifth Order Linear Partial Differential Equations with Parameter”, Lobachevskii J Math, 45:10 (2024), 5313  crossref
    3. Zh. Sartabanov, G. A. Abdikalikova, G. M. Aitenova, B. Zh. Omarova, A. Kh. Zhumagaziyev, “Implementation of the Small Parameter Method for Studying Multiperiodic Solutions of Systems with a Diagonal Differentiation Operator”, Lobachevskii J Math, 45:12 (2024), 6594  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. A. K. Urinov, A. B. Okboev, “On a Cauchy Type Problem for a Second Kind Degenerating Hyperbolic Equation”, Lobachevskii J Math, 43:3 (2022), 793  crossref
    6. D. Amanov, O. Sh. Kilichov, “Nonlocal Boundary Value Problem for a Fourth Order Differential Equation”, Lobachevskii J Math, 43:2 (2022), 293  crossref
    7. T. K. Yuldashev, F. D. Rakhmonov, “On a Benney–Luke Type Differential Equation with Nonlinear Boundary Value Conditions”, Lobachevskii J Math, 42:15 (2021), 3761  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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