Stability for thermo-elastic Bresse system of second sound with past history and delay term

Abstract

We consider a one-dimensional linear thermo-elastic system of Bresse type with past history and delay term . We prove the well-posedness of problem using the semigroup method. By using the energy method, we discuss stability of the system for two cases. An exponential stability result is obtained in the case where the propagation velocities are equal in equation of vertical displacement and the equation of system rotation angle . Furthermore, a result of algebraic stability is obtained in the case of the different propagation velocities , where the initial data E2(0) is involved in the decay rate for the case.