Chaotic behaviour of the solutions of the Moore-Gibson-Thompson equation
[EN] We study a third-order partial differential equation in the form $\tau u_{ttt} +\alpha u_{tt} -c^2 u_{xx} -b u_{xxt} =0, (1)$$ that corresponds to the one-dimensional version of the Moore-Gibson-Thompson equation arising in high-intensity ultrasound and linear vibrations of elastic structures....
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/64842 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/64842 |
| Access Level: | acceso abierto |
| Palabra clave: | Acoustics C0-semigroups Devaney chaos Hypercyclicity Moore-Gibson-Thompson equation Sound propagation MATEMATICA APLICADA |
| Sumario: | [EN] We study a third-order partial differential equation in the form $\tau u_{ttt} +\alpha u_{tt} -c^2 u_{xx} -b u_{xxt} =0, (1)$$ 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 $\gamma:=\alpha-\frac{\tauc^2}{b}$ 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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