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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 4, Pages 621–648
DOI: https://doi.org/10.1134/S0044466919040069 (Mi zvmmf10880) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Blow-up of solutions of nonclassical nonlocal nonlinear model equations

M. O. Korpusovab

a Faculty of Physics, Moscow State University, Moscow, 119992 Russia
b RUDN University, Moscow, 117198 Russia
Citations (2)
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DOI: https://doi.org/10.1134/S0044466919040069
Abstract: For a nonlinear nonlocal operator differential equation of the first order, an abstract Cauchy problem is considered that is a generalization of certain model physical examples. For this problem, the existence of a nonextendable (in time) classical solution is proved. Additionally, finite-time blow-up results are obtained under certain sufficient conditions, and bilateral estimates for the blow-up time are derived. Finally, under certain conditions, the problem is proved to be globally well posed regardless of the value of the initial function.
Key words: nonlinear Sobolev-type equations, blow-up, local solvability, nonlinear capacity, estimates of the blow-up time.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 5-100
This work was supported by the RUDN University program 5-100.
Received: 01.12.2016
Revised: 16.06.2017
Accepted: 14.11.2018
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 4, Pages 583–609
DOI: https://doi.org/10.1134/S0965542519040067
Bibliographic databases:
Document Type: Article
UDC: 517.538
Language: Russian
Citation: M. O. Korpusov, “Blow-up of solutions of nonclassical nonlocal nonlinear model equations”, Zh. Vychisl. Mat. Mat. Fiz., 59:4 (2019), 621–648; Comput. Math. Math. Phys., 59:4 (2019), 583–609
Citation in format AMSBIB
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    • This publication is cited in the following 2 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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