Chaotic Behaviour of the Solutions of the Moore-Gibson-Thompson Equation

We study a third-order partial differential equation in the form tuttt + αutt - c2uxx - buxxt = 0, that corresponds to the one-dimensional version of the Moore-Gibson-Thompson equation arising in high-intensity ultrasound and linear vibrations of elastic structures. In contrast with the current literature on the subject, we show that when the critical parameter γ : = α - t c2/b is negative, the equation (1) admits an uniformly continuous, chaotic and topologically mixing semigroup on Banach spaces of Herzog s type. © 2015 NSP Natural Sciences Publishing Cor.