Gevrey regularity for the Euler–Bernoulli beam equation with localized structural damping

Abstract

We study a Euler–Bernoulli beam equation with localized discontinuous structural damping. As our main result, we prove that the associated C 0 -semigroup ( S ( t ) ) t ≥ 0 is of Gevrey class δ > 24 for t>0, hence immediately differentiable. Moreover, we show that ( S ( t ) ) t ≥ 0 is exponentially stable.