Optimal scalar products in the Moore-Gibson-Thompson equation
We study the third order in time linear dissipative wave equation known as the Moore-Gibson-Thompson equation, that appears as the lineariza-tion of a the Jordan-Moore-Gibson-Thompson equation, an important model in nonlinear acoustics. The same equation also arises in viscoelasticity theory, as a m...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10256/17123 |
| Acceso en línea: | http://hdl.handle.net/10256/17123 |
| Access Level: | acceso abierto |
| Palabra clave: | Equacions diferencials parcials Differential equations, Partial Equacions de Moore-Gibson-Thompson Moore-Gibson-Thompson equations |
| Sumario: | We study the third order in time linear dissipative wave equation known as the Moore-Gibson-Thompson equation, that appears as the lineariza-tion of a the Jordan-Moore-Gibson-Thompson equation, an important model in nonlinear acoustics. The same equation also arises in viscoelasticity theory, as a model which is considered more realistic than the usual Kelvin-Voigt one for the linear deformations of a viscoelastic solid. In this context, it is known as the Standard Linear Viscoelastic model. We complete the description in [13] of the spectrum of the generator of the corresponding group of operators and show that, apart from some exceptional values of the parameters, this generator can be made to be a normal operator with a new scalar product, with a complete set of orthogonal eigenfunctions. Using this property we also obtain optimal exponential decay estimates for the solutions as t → ∞, whether the operator is normal or not |
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