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 linearization of a the Jordan-Moore-Gibson-Thompson equation, an important model in nonlinear acoustics. The same equation also arises in viscoelasticity theory, as a mo...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/130655 |
| Acceso en línea: | https://hdl.handle.net/2117/130655 https://dx.doi.org/10.3934/eect.2019011 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential equations, Partial Moore-Gibson-Thompson equation standard linear viscoelastic model normal operator optimal exponential decay. Equacions diferencials parcials Classificació AMS::35 Partial differential equations Classificació AMS::47 Operator theory::47D Groups and semigroups of linear operators, their generalizations and applications Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | We study the third order in time linear dissipative wave equation known as the Moore-Gibson-Thompson equation, that appears as the linearization 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¿8, whether the operator is normal or not. |
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