RUS  ENG
Full version
JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2020 Volume 61, Number 1, Pages 60–77 (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

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.

UDC: 517.958

MSC: 35R30

Received: 15.01.2019
Revised: 15.01.2019
Accepted: 15.05.2019

DOI: 10.33048/smzh.2020.61.104


 English version:
Siberian Mathematical Journal, 2020, 61:1, 47–61

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024