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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 1, Pages 60–77
DOI: https://doi.org/10.33048/smzh.2020.61.104 (Mi smj5964) 		 
Evolutionary problems of nonlinear magnetoelasticity

M. P. Vishnevskiiab, V. I. Priimenkob

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b North Fluminense State University
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DOI: https://doi.org/10.33048/smzh.2020.61.104
Abstract: We consider mixed problems for nonlinear equations of magnetoelasticity. Our main result in the three-dimensional case is the proof of an existence and uniqueness theorem; uniqueness is established under some extra restrictions on the smoothness of solutions. We also manage to prove the existence and uniqueness of a weak solution to the problem in the two-dimensional case; uniqueness is established without any additional a priori assumptions on the smoothness of solutions.
Keywords: nonlinear magnetoelastic effect, mixed problem, existence and uniqueness theorems.
Funding agency Grant number
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro E-26/010.001037/2016
The authors were partially supported by Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (Grant E—26/010.001037/2016).
Received: 15.01.2019
Revised: 15.01.2019
Accepted: 15.05.2019
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 1, Pages 47–61
DOI: https://doi.org/10.1134/S0037446620010048
Bibliographic databases:
Document Type: Article
UDC: 517.958
MSC: 35R30
Language: Russian
Citation: M. P. Vishnevskii, V. I. Priimenko, “Evolutionary problems of nonlinear magnetoelasticity”, Sibirsk. Mat. Zh., 61:1 (2020), 60–77; Siberian Math. J., 61:1 (2020), 47–61
Citation in format AMSBIB
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\by M.~P.~Vishnevskii, V.~I.~Priimenko
\paper Evolutionary problems of nonlinear magnetoelasticity
\jour Sibirsk. Mat. Zh.
\yr 2020
\vol 61
\issue 1
\pages 60--77
\mathnet{http://mi.mathnet.ru/smj5964}
\crossref{https://doi.org/10.33048/smzh.2020.61.104}
\transl
\jour Siberian Math. J.
\yr 2020
\vol 61
\issue 1
\pages 47--61
\crossref{https://doi.org/10.1134/S0037446620010048}
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