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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 10, Pages 1639–1661
DOI: https://doi.org/10.31857/S0044466922090071 (Mi zvmmf11458) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Partial Differential Equations

Local solvability, blow-up, and Hölder regularity of solutions to some Cauchy problems for nonlinear plasma wave equations: I. Green formulas

M. O. Korpusov, E. A. Ovsyannikov

Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia
Citations (2)
DOI: https://doi.org/10.31857/S0044466922090071
Abstract: Three nonlinear equations for ion acoustic and drift waves in a plasma are derived. The fundamental solution of the common linear part of the resulting nonlinear equations is constructed, and its smoothness properties are studied. Next, the second Green formula in a bounded domain is constructed, which is then used to derive the third Green formula in a bounded domain. Finally, two variants of the third Green formula in the entire space are constructed in a certain class of functions.
Key words: nonlinear Sobolev-type equations, fundamental solution, Green formulas.
Funding agency Grant number
Foundation for the Advancement of Theoretical Physics and Mathematics BASIS
RUDN University Strategic Academic Leadership Program
This work was supported by the Foundation for Advancement of Theoretical Physics and Mathematics “BASIS” and by the RUDN Program of Strategic Academic Leadership.
Received: 29.11.2021
Revised: 11.03.2022
Accepted: 11.04.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 10, Pages 1609–1631
DOI: https://doi.org/10.1134/S096554252209007X
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: M. O. Korpusov, E. A. Ovsyannikov, “Local solvability, blow-up, and Hölder regularity of solutions to some Cauchy problems for nonlinear plasma wave equations: I. Green formulas”, Zh. Vychisl. Mat. Mat. Fiz., 62:10 (2022), 1639–1661; Comput. Math. Math. Phys., 62:10 (2022), 1609–1631
Citation in format AMSBIB
\Bibitem{KorOvs22}
\by M.~O.~Korpusov, E.~A.~Ovsyannikov
\paper Local solvability, blow-up, and H\"older regularity of solutions to some Cauchy problems for nonlinear plasma wave equations: I. Green formulas
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 10
\pages 1639--1661
\mathnet{http://mi.mathnet.ru/zvmmf11458}
\crossref{https://doi.org/10.31857/S0044466922090071}
\elib{https://elibrary.ru/item.asp?id=49344330}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 10
\pages 1609--1631
\crossref{https://doi.org/10.1134/S096554252209007X}
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