Well‐Posedness and Stability of Delayed Abstract Thermoelastic Systems

ABSTRACT In this paper, we consider a stabilization problem of a generalized thermoelastic system (the so called – system) with delay in a part of the coupled system. For each case, we prove the well‐posedness of the corresponding system using semigroup approach, then under some sufficient conditions we establish some results of exponential and polynomial stability of the system through a frequency‐domain approach. The results are applied to concrete examples in thermoelasticity.