Asymptotic Analysis of an Abstract Timoshenko System: Semigroup Stability, Analyticity and Gevrey Class

Rodrigo Nunes Monteiro - Universidade Estadual de Londrina, Brasil

Abstract:

This talk addresses an abstract Timoshenko system with fractional damping, modeled by powers of a strictly positive self-adjoint operator densely defined in a Hilbert space. The system is reformulated as a first-order evolution equation, and the associated operator is shown to generate a strongly continuous semigroup. Depending on the fractional powers, the semigroup may exhibit exponential stability, analyticity, or belong to a specific Gevrey class. The Gevrey class obtained is proven to be sharp.