We study a third-order partial differential equation in the form t uttt +autt −c2uxx −buxxt = 0, (1) 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 g := a − t c2 b is negative, the equation (1) admits an uniformly continuous, chaotic and topologically mixing semigroup on Banach spaces of Herzog’s type.
Alberto Conejero, J.; Lizama, Carlos; and Rodenas, Francisco
"Chaotic Behaviour of the Solutions of the Moore-Gibson- Thompson Equation,"
Applied Mathematics & Information Sciences: Vol. 09
, Article 3.
Available at: https://dc.naturalspublishing.com/amis/vol09/iss5/3