Abstract
In this work we show that the energy associated to the linear three-dimensional magneto-elastic system decays polynomially to zero as time goes to infinity, provided the initial data is smooth enough.
Similar content being viewed by others
References
Andreou, E. and Dassios, G.: Dissipation of energy for magnetoelastic waves in a conductive medium, Quart.Appl.Math. 55 (1997), 23–39.
Duvaut, G. and Lions, J. L.: Inequalities in Mechanics and Physics, Grundlehren Math. Wiss. 216, Springer-Verlag, Berlin, 1976.
Erigen, C. A. and Maugin, G. A.: Eletrodynamics of Continua I, Springer-Verlag, New York, 1990.
Koch, H.: Slow decay in linear thermoelasticity, Quart.J.Appl.Math. 57(4) (2000), 601–612.
Lebeau, G. and Zuazua, E.: Decay rates for the three-dimensional linear system of thermoelasticity, Arch.Rat.Mech.Anal. 145 (1999), 179–231.
Leis, R.: Initial Boundary Value Problems in Mathematical Physics, B. G. Teubner-Verlag, Stuttgart; Wiley, Chichester, 1986.
Muñoz Rivera, J. E. and Racke, R.: Magneto-thermoelasticity-large time behavior for linear system, Adv.Differential Equations 6 (2001), 359–384.
Muñoz Rivera, J. E. and Racke, R.: Polynomial stability in two-dimensional magneto-elasticity, IMA J.Appl.Math. 66 (2001), 269–283.
Pazy, A.: Semigroups of Linear Operators and Applications to Partial Diferential Equations, Springer, New York, 1983.
Perla Menzala, G. and Zuazua, E.: Energy decay of magnetoelastic waves in a bounded conductive medium, Asymptot.Anal. 18 (1998), 349–362.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Muñoz Rivera, J.E., de Lima Santos, M. Polynomial Stability to Three-Dimensional Magnetoelastic Waves. Acta Applicandae Mathematicae 76, 265–281 (2003). https://doi.org/10.1023/A:1023223517930
Issue Date:
DOI: https://doi.org/10.1023/A:1023223517930