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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 5, Pages 1091–1101 (Mi smj2332)  

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

On some method for solving a nonlinear heat equation

L. I. Rubinaa, O. N. Ul'yanovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University, Ekaterinburg
References:
Abstract: Some exact solutions to a nonlinear heat equation are constructed. An initial-boundary value problem is examined for a nonlinear heat equation. To construct solutions, the problem for a partial differential equation of the second order is reduced to a similar problem for a first order partial differential equation.
Keywords: nonlinear partial differential equations, heat equation, boundary value problem, initialboundary value problem.
Received: 16.03.2011
Revised: 25.01.2012
English version:
Siberian Mathematical Journal, 2012, Volume 53, Issue 5, Pages 872–881
DOI: https://doi.org/10.1134/S0037446612050126
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: L. I. Rubina, O. N. Ul'yanov, “On some method for solving a nonlinear heat equation”, Sibirsk. Mat. Zh., 53:5 (2012), 1091–1101; Siberian Math. J., 53:5 (2012), 872–881
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/smj2332
  • https://www.mathnet.ru/eng/smj/v53/i5/p1091
  • This publication is cited in the following 14 articles:
    1. Alexander Kazakov, Anna Lempert, “Multidimensional Diffusion-Wave-Type Solutions to the Second-Order Evolutionary Equation”, Mathematics, 12:2 (2024), 354  crossref
    2. S. A. Zinina, A. I. Popov, A. V. Eremin, “Chislennoe reshenie nelineinoi zadachi teploprovodnosti v poristoi plastine s uporyadochennoi makrostrukturoi”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2024, no. 1, 53–67  mathnet  crossref  elib
    3. A. L. Kazakov, “Resheniya c nulevym frontom dlya kvazilineinogo parabolicheskogo uravneniya teploprovodnosti”, Tr. IMM UrO RAN, 30, no. 2, 2024, 86–102  mathnet  crossref  elib
    4. S. P. Bautin, I. A. Vazieva, “PREDSTAVLENIE REShENII ODNOMERNOGO NELINEINOGO URAVNENIYa TEPLOPROVODNOSTI TRIGONOMETRIChESKIMI RYaDAMI”, Vestnik, 13:3 (2024), 154  crossref
    5. A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “The Problem of Diffusion Wave Initiation for a Nonlinear Second-Order Parabolic System”, Proc. Steklov Inst. Math. (Suppl.), 321, suppl. 1 (2023), S109–S126  mathnet  crossref  crossref  mathscinet  elib
    6. L. I. Rubina, “Ob odnom podkhode k resheniyu volnovogo uravneniya dlya dielektricheskikh nemagnitnykh sred”, Tr. IMM UrO RAN, 29, no. 2, 2023, 145–156  mathnet  crossref  mathscinet  elib
    7. A. L. Kazakov, A. A. Lempert, “Tochnye resheniya tipa diffuzionnykh voln dlya nelineinogo vyrozhdayuschegosya parabolicheskogo uravneniya vtorogo poryadka”, Tr. IMM UrO RAN, 28, no. 3, 2022, 114–128  mathnet  crossref  elib
    8. L. I. Rubina, O. N. Ulyanov, “On double wave type flows”, Siberian Math. J., 60:4 (2019), 673–684  mathnet  crossref  crossref  isi  elib
    9. A. L. Kazakov, P. A. Kuznetsov, “On the analytic solutions of a special boundary value problem for a nonlinear heat equation in polar coordinates”, J. Appl. Industr. Math., 12:2 (2018), 255–263  mathnet  crossref  crossref  elib  elib
    10. L. I. Rubina, O. N. Ul'yanov, “On the problem of the flow of an ideal gas around bodies”, Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 145–154  mathnet  crossref  crossref  isi  elib
    11. L. I. Rubina, O. N. Ulyanov, “Ob odnom podkhode k resheniyu neodnorodnykh uravnenii v chastnykh proizvodnykh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:3 (2017), 355–364  mathnet  crossref  elib
    12. L. I. Rubina, O. N. Ulyanov, “Dva podkhoda k resheniyu uravneniya potentsiala v avtomodelnykh peremennykh”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:3 (2015), 30–38  mathnet  elib
    13. Rubina L.I., Ul'yanov O.N., “on Solving Certain Nonlinear Acoustics Problems”, Acoust. Phys., 61:5 (2015), 527–533  crossref  isi  elib  scopus
    14. A. I. Korotkii, N. A. Artemova, N. A. Vaganova, O. O. Kovrizhnykh, L. I. Rubina, O. N. Ulyanov, O. V. Ushakova, M. Yu. Filimonov, I. A. Tsepelev, “O razrabotkakh analiticheskikh i chislennykh metodov resheniya zadach mekhaniki sploshnoi sredy”, Tr. IMM UrO RAN, 19, no. 2, 2013, 203–215  mathnet  mathscinet  elib
    Citing articles in Google Scholar: Russian citations, English citations
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