Elastic and electro-magnetic waves in infinite waveguides

We consider initial–boundary value problems for the equations of isotropic elasticity for several mixed boundary conditions in infinite wave guides, as well as Maxwell equations. With the help of decompositions of the displacement field into divergence- and curl-free parts, respectively, which are compatible with the boundary conditions, we obtain sharp decay rates for the solutions. The decomposed systems correspond to the second-order Maxwell equations for the electric and the magnetic field with electric and magnetic boundary conditions, respectively.