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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 9 > No. 5


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

PP: 2233-2238
J. Alberto Conejero, Carlos Lizama, Francisco Rodenas,
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.

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