Existence and energy decay of a Bresse system with thermoelasticity of type III

Abstract

In this paper, we investigate a one-dimensional thermoelastic Bresse system, where the heat conduction is given by Green and Naghdi theories. Under some assumptions on the memory kernel and a new introduced stability number, we prove that the unique damping given by the memory term is sufficiently strong to stabilize the system exponentially. In fact, we establish a general decay result from which the exponential and polynomial decays are only special cases.

Exponential stability for porous thermoelastic systems with Gurtin-Pipkin flux

“…(1.10) Fatori and Rivera [16] showed the Bresse-Fourier system was exponentially stable if and only if k = k 0 and (1.9) holds. For a discussion of the type III thermoelastic Bresse system readers may refer to [17] which considered the effect of memory item.…”