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

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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. Rubina^a, O. N. Ul'yanov^ab

^a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
^b Ural Federal University, Ekaterinburg

Full-text PDF (272 kB) Citations (14)

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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

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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:

Alexander Kazakov, Anna Lempert, “Multidimensional Diffusion-Wave-Type Solutions to the Second-Order Evolutionary Equation”, Mathematics, 12:2 (2024), 354
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
A. L. Kazakov, “Resheniya c nulevym frontom dlya kvazilineinogo parabolicheskogo uravneniya teploprovodnosti”, Tr. IMM UrO RAN, 30, no. 2, 2024, 86–102
S. P. Bautin, I. A. Vazieva, “PREDSTAVLENIE REShENII ODNOMERNOGO NELINEINOGO URAVNENIYa TEPLOPROVODNOSTI TRIGONOMETRIChESKIMI RYaDAMI”, Vestnik, 13:3 (2024), 154
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
L. I. Rubina, “Ob odnom podkhode k resheniyu volnovogo uravneniya dlya dielektricheskikh nemagnitnykh sred”, Tr. IMM UrO RAN, 29, no. 2, 2023, 145–156
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
L. I. Rubina, O. N. Ulyanov, “On double wave type flows”, Siberian Math. J., 60:4 (2019), 673–684
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
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
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
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
Rubina L.I., Ul'yanov O.N., “on Solving Certain Nonlinear Acoustics Problems”, Acoust. Phys., 61:5 (2015), 527–533
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

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

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