Asymptotic stability of thermoelastic systems of Bresse type

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. Our main theorem also subsumes some recent achievements in the stability properties of thermoelastic Timoshenko systems with classical and nonclassical heat conduction.