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

摘要

In the present paper we consider the Standard Linear Solid model in R N 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.