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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 6, Pages 1006–1021
DOI: https://doi.org/10.31857/S0044466923060133 (Mi zvmmf11574) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Partial Differential Equations

On critical exponents for weak solutions of the Cauchy problem for a $(2+1)$-dimensional nonlinear composite-type equation with gradient nonlinearity

M. O. Korpusova, A. K. Matveevaab

a Faculty of Physics, Lomonosov Moscow State University, 119992, Moscow, Russia
b National Engineering Physics Institute "MEPhI", 115409, Moscow, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466923060133
Abstract: The Cauchy problem for a model nonlinear equation with gradient nonlinearity is considered. We prove the existence of two critical exponents, $q_1=2$ and $q_2=3$, such that this problem has no local-in-time weak (in some sense) solution for $1<q\le q_1$, while such a solution exists for $q>q_1$, but, for $q_1<q\le q_2$, there is no global-in-time weak solution.
Key words: nonlinear Sobolev-type equations, blow-up, local solvability, nonlinear capacity, blow-up time estimates.
Funding agency Grant number
Foundation for the Advancement of Theoretical Physics and Mathematics BASIS
Russian Science Foundation 23-11-00056
This work was supported by the Foundation for Advancement of Theoretical Physics and Mathematics “BASIS” and by the Russian Science Foundation (project no. 23-11-00056), RUDN University.
Received: 04.05.2022
Revised: 22.12.2022
Accepted: 03.03.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 6, Pages 1070–1084
DOI: https://doi.org/10.1134/S096554252306012X
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: M. O. Korpusov, A. K. Matveeva, “On critical exponents for weak solutions of the Cauchy problem for a $(2+1)$-dimensional nonlinear composite-type equation with gradient nonlinearity”, Zh. Vychisl. Mat. Mat. Fiz., 63:6 (2023), 1006–1021; Comput. Math. Math. Phys., 63:6 (2023), 1070–1084
Citation in format AMSBIB
\Bibitem{KorMat23}
\by M.~O.~Korpusov, A.~K.~Matveeva
\paper On critical exponents for weak solutions of the Cauchy problem for a $(2+1)$-dimensional nonlinear composite-type equation with gradient nonlinearity
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 6
\pages 1006--1021
\mathnet{http://mi.mathnet.ru/zvmmf11574}
\crossref{https://doi.org/10.31857/S0044466923060133}
\elib{https://elibrary.ru/item.asp?id=53836703}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 6
\pages 1070--1084
\crossref{https://doi.org/10.1134/S096554252306012X}
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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