Exponential stability for thermoelastic Bresse systems with nonclassical heat conduction

We provide a comprehensive stability analysis of the thermoelastic Bresse system (also known as the circular arch problem). In particular, assuming a temperature evolution of Gurtin-Pipkin type, we establish a necessary and sufficient condition for exponential stability in terms of the structural parameters of the problem. As a byproduct, a complete characterization of the longtime behavior of Bresse-type systems with Fourier, Maxwell-Cattaneo and Coleman-Gurtin thermal laws is obtained.