Well-posedness and decay property of regularity-loss type for the Cauchy problem of the standard linear solid model with Gurtin–Pipkin thermal law

Abstract

In this paper, we consider the Cauchy problem related to the standard linear solid model with Gurtin–Pipkin thermal law in the whole space. Under some assumptions on the relaxation function g, we establish the well-posedness result by using semigroup theory. Besides, by using the energy method in the Fourier space, we prove the decay estimate result under the non-critical case. Our result indicates that the decay property is of the regularity-loss type, which is in line with the decay property of Cattaneo system.