On the Double Moore–Gibson–Thompson System of Thermoviscoelasticity

ABSTRACT In this paper, we address the system made by two coupled one‐dimensional Moore–Gibson–Thompson equations arising in the description of thermoviscoelastic materials. Here, while . When both the MGT equations lie in the subcritical regime, that is, we prove that the system generates an exponentially stable solution semigroup. This improves some recent results in the literature, where the exponential stability is attained only within either a stronger condition than subcriticality of both equations, or when and are sufficiently close. The key idea is to deduce the exponential stability from that of a related system, made by two coupled equations of the viscoelasticity type. The latter result has also an independent interest.