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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 11, Pages 1870–1875
DOI: https://doi.org/10.7868/S0044466915110046 (Mi zvmmf10297) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On exact solutions of a nonclassical partial differential equation

A. I. Aristov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia
Full-text PDF (84 kB) Citations (5)
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DOI: https://doi.org/10.7868/S0044466915110046
Abstract: For a nonclassical nonlinear partial differential equation, several classes of solutions expressed in terms of elementary and special functions are constructed. Moreover, solutions of one of the classes contain an arbitrary sufficiently smooth function of a single argument. It is shown that, among these solutions, there are ones going to infinity in a finite time (blowing up) and ones that are bounded on any finite time interval.
Key words: nonlinear partial differential equations, exact solutions, solution blowup.
Received: 26.01.2015
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 11, Pages 1836–1841
DOI: https://doi.org/10.1134/S0965542515110044
Bibliographic databases:
Document Type: Article
UDC: 519.63
MSC: Primary 35G20; Secondary 35B44, 35C05
Language: Russian
Citation: A. I. Aristov, “On exact solutions of a nonclassical partial differential equation”, Zh. Vychisl. Mat. Mat. Fiz., 55:11 (2015), 1870–1875; Comput. Math. Math. Phys., 55:11 (2015), 1836–1841
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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