Fayssal Djellali

This paper studies a one-dimensional thermoelastic Bresse beam model, in which thermal effects governed by the Green–Naghdi theory of heat conduction are coupled specifically with the longitudinal displacement. Assuming appropriate conditions on the memory kernel and by defining a key stability parameter, we prove a unified decay estimate for the system’s energy. This general result includes both exponential and polynomial decay rates as special instances, offering a comprehensive framework for characterizing the system’s long-term behavior.

The present article investigates a one dimensional thermoelastic laminated beam with microtemperature effects. Using the energy method we prove in the case of zero thermal conductivity that the unique dissipation due to the microtemperatures is strong enough to exponentially stabilize the system if and only if the wave speeds of the system are equal. Our result is new and improves previous results in the literature.

In this work, we investigate a Bresse system with thermal and mass diffusion effects. First, we establish the existence of a unique solution for the problem using the semigroup theory. Then, we show the lack of exponential stability in the case of different wave speeds. Finally, we prove an exponential stability for the considered problem in the case of equal wave speeds.