Spatial Behavior and Continuous Dependence Results in the Linear Dynamic Theory of Magnetoelectroelasticity

This paper is concerned with some general theorems for the linear dynamic theory of magnetoelectroelasticity. First, the spatial behavior of solutions is studied. In this sense, the so called ??support?? of the given data in a fixed interval of time 0,T] is introduced and an adequate time-weighted surface power function associated with the solution at issue is considered. Using their properties, we get the domain of influence and an exponential decay estimate with time-independent rates inside the domain of influence. As a by-product, a uniqueness result is derived for both bounded and unbounded bodies. Then, the case of non-zero initial conditions is also considered. Under a boundedness restriction on the initial data, an energy estimate is obtained. Finally, a continuous dependence result of solutions upon initial data and body forces is established.