End effects in the dynamical problem of magneto-elasticity

In this paper we derive spatial decay bounds for the solutions of the linear dynamical problem of magneto-elasticity in a semi-infinite cylindrical region. For the forward-in-time problem we prove that an energy expression is bounded from above by a decaying exponential of a quadratic polynomial of the distance. We derive a spatial decay estimate for the backward-in-time problem as well. The proof works only if the cross-section is a finite union of rectangles with axes parallels to Ox2 and Ox3. As a conclusion we consider the extension of the preceding bound to the heat conduction case.