Abstract
We prove the theorem on the existence and uniqueness of global solutions of a system of semilinear magnetoelasticity equations in a two-dimensional space.
Similar content being viewed by others
References
O. M. Botsenyuk, “On the solvability of an initial boundary-value problem for a system of semilinear magnetoelasticity equations,” Ukr. Mat. Zh., 44, No. 9, 1181–1185 (1992).
J.-L. Lions and E. Magenes, Non-Homogeneous Boundary-Value Problems and Applications [Russian translation], Mir, Moscow 1971.
J.-L. Lions and E. Magenes, Non-Homogeneous Boundary-Value Problems and Applications, Springer, Berlin 1972.
P. Grisvard, “Caracterisation de quelques espaces d’interpolation,” Arch. Ration. Mech. Anal., 25, 40–63 (1967).
H. Triebel, Interpolation Theory. Function Spaces. Differential Operators [Russian translation], Mir, Moscow 1980.
J. Bergh and J. Lofstrom, Interpolation Spaces. An Introduction [Russian translation], Mir, Moscow 1980.
H. Engler, “An alternative proof of the Brezis-Wainger inequality,” Commun. Part. Different. Equat., 14, No. 4, 5451–5544 (1989).
H. Brezis and T. Gallouet, “Nonlinear Schrodinger evolution equations,” J. Nonlin. Anal, 4, No. 4, 677–681 (1980).
H. Brezis and S. Wainger, “A note on limiting cases of Sobolev imbeddings,” Commun. Part. Different. Equat., 5, 773–789 (1980).
Rights and permissions
About this article
Cite this article
Botsenyuk, O.M. Global solutions of a two-dimensional initial boundary-value problem for a system of semilinear magnetoelasticity equations. Ukr Math J 48, 181–188 (1996). https://doi.org/10.1007/BF02372044
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02372044