Decay and other estimates for a semi-infinite magnetoelastic cylinder: Saint-Venant's principle

An analogue of well known Toupin's version of Saint-Venant's principle is proved for a semi-infinite magnetoelastic cylinder under very mild assumptions on the asymptotic behaviour of the Dirichlet integral of the magnetic field anf of the elastic energy. With regard to the elastic fields, we assign on the base either the stress or the displacement vector while we assume that the lateral surface is either traction free or held fixed at zero displacement. We make use of the first Korn inequality and we estimate the total energy of the conductor in terms of the data for all the problems considered.