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

Authors

J. Alberto Conejero, Instituto Universitario de Matem´atica Pura y Aplicada, Universitat Polit´ecnica de Val`encia, Val`encia, SpainFollow
Carlos Lizama, Departamento de Matem´atica y Ciencia de la Computaci´on. Universidad de Santiago de Chile, Santiago, ChileFollow
Francisco Rodenas, Instituto Universitario de Matem´atica Pura y Aplicada, Universitat Polit´ecnica de Val`encia, Val`encia, SpainFollow

Author Country (or Countries)

Spain

Abstract

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.

Recommended Citation

Alberto Conejero, J.; Lizama, Carlos; and Rodenas, Francisco (2023) "Chaotic Behaviour of the Solutions of the Moore-Gibson- Thompson Equation," Applied Mathematics & Information Sciences: Vol. 09: Iss. 5, Article 3.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss5/3