Regularity and Stabilization of Magneto-Elastic Systems

We consider the mathematical model for a plate in a bounded reference configuration \(\Omega \subset \mathbb {R}^n\), first with \(n=2\), which is interacting with \(n=2\) magnetic fields. The latter have a damping effect. It will be shown that the arising system generates an analytic semigroup and that the estimated exponential decay rate tends to zero if the n constant directing magnetic vectors tend to become linearly dependent. Then, an analogous model for \(n=3\) will be considered. In the case that there are less than n magnetic fields we prove the strong stability exemplarily for cubes.