On the Cauchy problem of the standard linear solid model with Cattaneo heat conduction

Article type: Research Article

Authors: Pellicer, Marta^{a; *} | Said-Houari, Belkacem^b

Affiliations: [a] Dpt. d’Informàtica, Matemàtica Aplicada i Estadística (EPS), Universitat de Girona, Campus de Montilivi, 17071 Girona, Catalunya, Spain. E-mail: martap@imae.udg.edu | [b] Department of Mathematics, College of Sciences, University of Sharjah, P.O. Box: 27272, Sharjah, United Arab Emirates. E-mail: bsaidhouari@gmail.com

Correspondence: [*] Corresponding author. E-mail: martap@imae.udg.edu.

Abstract: In the present paper we consider the Standard Linear Solid model in RN coupled with the Cattaneo law of heat conduction. We show the well-posedness and asymptotic stability of the problem, giving decay rates for a norm related to the solution. These results are compared with those given for the Fourier problem in (Pellicer and Said-Houari (2020)) and the ones of the problem without heat conduction (see previous work (Appl Math. Optim 80 (2019) 447–478)). The main difference is that the Cattaneo system exhibits the well-known regularity-loss phenomenon. The methods used to prove these results are the energy method in the Fourier space and the eigenvalues expansion method.

Keywords: Standard Linear Solid model, Moore–Gibson–Thompson equation, Cattaneo heat conduction, decay rate, asymptotic stability, regularity-loss

DOI: 10.3233/ASY-201666

Journal: Asymptotic Analysis, vol. 126, no. 1-2, pp. 95-127, 2022