On a Fourth-Order Equation of Moore–Gibson–Thompson Type - Dell’Oro, Filippo; Pata, Vittorino (Milan journal of mathematics, 2017)
An abstract version of the fourth-order equation ∂ t t t t u + α ∂ t t t u + β ∂ t t u - γ Δ ∂ t t u - δ Δ ∂ t u - ϱ Δ u = 0 subject to the homogeneous Dirichlet boundary condition is analyzed. Such a model encompasses the Moore–Gibson–Thompson equation with memory in presence of an exponential kernel. The stability properties of the related solution semigroup are investigated. In particular, a necessary and sufficient condition for exponential stability is established, in terms of the values of certain stability numbers depending on the strictly positive parameters α , β , γ , δ , ϱ .