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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Volume 18, Number 2, Pages 265–280
(Mi timm828)
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This article is cited in 7 scientific papers (total in 7 papers)
Solution of nonlinear partial differential equations by the geometric method
L. I. Rubinaa, O. N. Ul'yanovab a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University
Abstract:
The earlier proposed geometric method of investigation of nonlinear partial differential equations is developed. The heat equation describing blow-up regimes and the equation for the flow function in a boundary layer are studied. We propose a modification of the method based on the specific character of the equations and show its applicability in the case under consideration. Classes of particular exact solutions are found and a boundary value problem is solved.
Keywords:
nonlinear partial differential equations, heat equation, equation for the flow function in a boundary layer, exact solutions.
Received: 08.09.2011
Citation:
L. I. Rubina, O. N. Ul'yanov, “Solution of nonlinear partial differential equations by the geometric method”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 265–280
Linking options:
https://www.mathnet.ru/eng/timm828 https://www.mathnet.ru/eng/timm/v18/i2/p265
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