Optimal scalar products in the Moore-Gibson-Thompson equation

Full Text
Postprint-PellicerSolaMoralesEECT.pdf embargoed access
Request a copy
When filling the form you are requesting a copy of the article, that is deposited in the institutional repository (DUGiDocs), at the autor or main autor of the article. It will be the same author who decides to give a copy of the document to the person who requests it, if it considers it appropriate. In any case, the UdG Library doesn’t take part in this process because it is not authorized to provide restricted articles.
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 ​
​Tots els drets reservats