New stability result for a thermoelastic Bresse system

In this paper, we investigate a one-dimensional Bresse system coupled with two thermal damping mechanisms working on the bending moment and the axial force and given by heat conduction of type III. By introducing two suitable stability numbers, we establish a general decay result for the associated energy through the construction of appropriate Lyapunov functionals. Moreover, the obtained decay estimate is sufficiently general to encompass several important decay rates as specific cases. In particular, exponential and polynomial decays are recovered according to the choice of relaxation functions, highlighting the influence of the memory kernels in determining the stability and decay properties of the system. The current obtained results are new and represent a substantial improvement over previously published findings in the literature.