Regularity and stability of two coupled Euler-Bernoulli equations with a localized singular structural damping

TL;DR

This paper investigates the regularity and stability of two coupled Euler-Bernoulli beam equations with localized singular damping, establishing Gevrey regularity and uniform stability under various damping conditions.

Contribution

It provides new results on the regularity and stability of coupled Euler-Bernoulli equations with localized singular damping, including cases with less regular damping mechanisms.

Findings

Gevrey regularity of the semigroup under regular damping assumptions

Uniform stability results for broader damping classes

Detailed description of long-term dynamical behavior

Abstract

This paper is concerned with the study of regularity and stability properties of two Euler-Bernoulli beam equations with localized singular damping. Under suitable regularity assumptions on the damping coefficient, we establish Gevrey regularity for the semigroup generated by the associated operator. Furthermore, for a broader class of damping mechanisms, including less regular damping, we derive uniform stability result. These findings provide a detailed description of the long-term behavior of the corresponding dynamical systems.