On the Double Moore–Gibson–Thompson System of Thermoviscoelasticity

In this paper we address the system made by two coupled one-dimensional Moore-Gibson-Thompson equations (u + alpha u - beta u(xx) - gamma u(xx) = p(alpha w(x) + w(x)) (w + alpha w - beta u(xx) - gamma w(xx) = p(alpha u(x) + u(x)) arising in the description of thermoviscoelastic materials. Here alpha, beta, gamma , alpha,beta,gamma > 0 while pp > 0. When both the MGT equations lie in the subcritical regime, that is, beta-gamma/alpha > 0 and beta -gamma/alpha > 0 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 alpha and alpha are suciently close. The key idea is to deduce the exponential stability from the one of a related system, made by two coupled equations of viscoelasticity type. The latter result has also an independent interest.