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.
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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 1, pp. 60–77.
The authors were partially supported by Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (Grant E—26/010.001037/2016).
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Vishnevskii, M.P., Priimenko, V.I. Evolutionary Problems of Nonlinear Magnetoelasticity. Sib Math J 61, 47–61 (2020). https://doi.org/10.1134/S0037446620010048
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DOI: https://doi.org/10.1134/S0037446620010048