Exponential Stabilization of a Nonlocal Micro‐Beam System

This paper is concerned with the exponential stabilization of a micro‐beam subject to the effect of a distributed memory term. In order to handle the nonlocal character of the problem, the minimal state approach is adopted. This allows us to show, on the one hand, that the problem is well‐posed in the sense of semigroup theory. On the other hand, the exponential stability of the solutions is established by means of the energy method. These outcomes extend the previous ones, where the impact of the memory phenomenon is disregarded.