We analyze the behavior as t → ∞ of strong solutions of the initial-boundary-value problem for a system of semilinear equations of magnetoelasticity with dissipative term in exterior domains. The estimates of energy decay are obtained. For the vector of magnetic induction, the estimates of decay are established in the spaces L∞ and L2.
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O. M. Botsenyuk, “Estimation of decay of the solutions of initial-boundary-value problem for the system of semilinear equations of magnetoelasticity in exterior domains,” Mat. Met. Fiz.-Mekh. Polya, 57, No. 4, 35–43 (2014); English translation: J. Math. Sci., 220, No. 1, 38–49 (2017); https://doi.org/10.1007/s10958-016-3166-6.
O. M. Botsenyuk, “On L2-estimates of decay of the solutions with respect to time of the initial-boundary-value problem for the system of semilinear equations of magnetoelasticity in exterior domains,” Mat. Met. Fiz.-Mekh. Polya, 43, No. 3, 51–55 (2000).
O. M. Botsenyuk, “On the solvability of the initial-boundary-value problem for the system of semilinear equations of magnetoelasticity,” Ukr. Mat. Zh., 44, No. 9, 1181–1186 (1992); English translation: Ukr. Math. J., 44, No. 9, 1080–1084 (1992); https://doi.org/10.1007/BF01058367.
O. M. Botsenyuk, “Regularity of solutions of an initial/boundary problem for a system of semilinear equations of magnetoelasticity,” Mat. Met. Fiz.-Mekh. Polya, Issue 38, 62–66 (1995); English translation: J. Math. Sci., 81, No. 6, 3053–3057 (1996); https://doi.org/10.1007/BF02362593.
B. P. Demidovich, Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).
R. C. Charão, J. C. Oliveira, and G. P. Menzala, “Decay rates of magnetoelastic waves in an unbounded conductive medium,” Electron. J. Differ. Equat., 2011, No. 127, 1–14 (2011).
M. V. Ferreira and G. P. Menzala, “Energy decay for solutions to semilinear systems of elastic waves in exterior domains,” Electron. J. Differ. Equat., 2006, No. 65, 1–13 (2006).
C. R. da Luz and J. C. Oliveira, “Asymptotic behavior of solutions for the magneto-thermo-elastic system in ℝ3,” J. Math. Anal. Appl., 432, No. 2, 1200–1215 (2015); https://doi.org/10.1016/j.jmaa.2015.07.014.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 65, No. 1-2, pp. 121–127, January–June, 2022.
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Botsenyuk, O.M. On Estimation of the Decay of Solutions of an Initial-Boundary-Value Problem for a System of Semilinear Equations of Magnetoelasticity with Dissipative Term in Exterior Domains. J Math Sci 282, 751–759 (2024). https://doi.org/10.1007/s10958-024-07213-x
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DOI: https://doi.org/10.1007/s10958-024-07213-x