On the analyticity of the abstract MGT-Fourier system

We consider the abstract MGT-Fourier system u ttt + α u tt + β A ϱ u t + γ A ϱ u = η A θ θ t + κ A θ = - η A u tt - η α A u t in the subcritical regime β > γ / α , where the operator A is strictly positive selfadjoint. For any fixed ϱ ∈ [ 1 , 2 ] , we show that the associated solution semigroup S ( t ) is analytic and exponentially stable as well.