This work is devoted to study the asymptotic behavior of the total energy associated with a coupled system of anisotropic hyperbolic models: the elastodynamic equations and Maxwell's system in the exterior of a bounded body in . Our main result says that in the presence of nonlinear damping, a unique solution of small initial data exists globally in time and the total energy as well as higher order energies decay at a uniform rate as .
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Cleverson Roberto da Luz, Gustavo Alberto Perla Menzala, Uniform decay rates of coupled anisotropic elastodynamic/Maxwell equations with nonlinear damping. Port. Math. 68 (2011), no. 2, pp. 205–238DOI 10.4171/PM/1889