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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 1, Pages 112–123 (Mi zvmmf9641)  
This article is cited in 27 scientific papers (total in 27 papers)

Mixed value problem for nonlinear integro-differential equation with parabolic operator of higher power

T. K. Yuldashev

SibSAU, Krasnoyarsky rabochy 31, Krasnoyarsk, 660014 Russia
Full-text PDF (239 kB) Citations (27)
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Abstract: We study the questions of one-valued solvability of mixed value problem for nonlinear integro-differential equation, consisting a parabolic operator of higher power. By the aid of Fourier series of separation variables the considering problem we can reduce to study the countable system of nonlinear integral equations, one-valued solvability of which will be proved by the method of successive approximations. The convergence of Fourier series will be studied by means of integral identity.
Key words: parabolic operator of higher power, Fourier series, integral identity, generalized derivatives, countable system of nonlinear integral equations, method of successive approximations.
Received: 24.05.2011
English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 1, Pages 105–116
DOI: https://doi.org/10.1134/S0965542512010150
Bibliographic databases:
Document Type: Article
UDC: 519.635
Language: Russian
Citation: T. K. Yuldashev, “Mixed value problem for nonlinear integro-differential equation with parabolic operator of higher power”, Zh. Vychisl. Mat. Mat. Fiz., 52:1 (2012), 112–123; Comput. Math. Math. Phys., 52:1 (2012), 105–116
Citation in format AMSBIB
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    • This publication is cited in the following 27 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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