Stability of a linear thermoelastic Bresse system with second sound under new conditions on the coefficients

Abstract

AbstractIn this paper, we discuss the stability of a linear one‐dimensional thermoelastic Bresse system, where the coupling is given through the first component of the Bresse model with the heat conduction of second sound type. We state the well‐posedness and show the polynomial stability of the system, where the decay rate depends on the smoothness of initial data. Moreover, we prove the non exponential and the exponential decay depending on new conditions on the parameters of the system. The proof is based on a combination of the energy method and the frequency domain approach.