Magneto-thermo-elasticity---large-time behavior for linear systems

Abstract

Initial and initial-boundary value problems for linearized magneto-thermo-elastic models are considered. For the Cauchy problem in three space dimensions, a polynomial rate of decay as time tends to infinity is proved. In bounded domains a boundary condition of memory type is considered for the displacement. When the relaxation function satisfies dissipative properties and decays exponentially, we show that the solution of the magneto-thermo-elastic system decays exponentially. When the relaxation function decays polynomially, it is proved that the solution decays polynomially. Energy methods are used.