Optimal scalar products in the Moore-Gibson-Thompson equation
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Data publicació2019-03-01
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Abstract
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.
CitacióPellicer, M.; Sola-morales, J. Optimal scalar products in the Moore-Gibson-Thompson equation. "Evolution Equations and Control Theory", 1 Març 2019, vol. 8, núm. 1, p. 203-220.
ISSN2163-2480
Versió de l'editorhttp://aimsciences.org//article/doi/10.3934/eect.2019011
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