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Chaotic Behaviour of the Solutions of the Moore-Gibson- Thompson Equation |
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PP: 2233-2238 |
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Author(s) |
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J. Alberto Conejero,
Carlos Lizama,
Francisco Rodenas,
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Abstract |
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| 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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