Lack of differentiability of semigroups associated to delayed abstract thermoelastic systems

TL;DR

This paper investigates the mathematical properties of semigroups related to delayed thermoelastic systems, demonstrating that these semigroups lack differentiability in certain Hilbert space settings.

Contribution

It provides a rigorous proof that semigroups associated with delayed thermoelastic systems are not differentiable, highlighting a fundamental limitation in their mathematical analysis.

Findings

Semigroups are not differentiable in the presence of delays.

The result applies to the { extalpha}-{ extbeta} thermoelastic system.

The analysis is conducted within appropriate Hilbert spaces.

Abstract

In this paper, we consider the associated semigroups to some abstract thermoelastic systems (in particular the {\alpha}-\b{eta} system), with a partial delay on the coupled system. We will prove that the corresponding semigroups (in appropriate Hilbert spaces) are not differentiable.