Abstract
An abstract version of the fourth-order equation $$\partial_{tttt}u+\alpha\partial_{ttt}u+\beta\partial_{tt}u-\gamma\Delta\partial_{tt}u-\delta\Delta\partial_{t}u-\varrho\Delta u=0$$ 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 $${\alpha, \beta, \gamma, \delta, \varrho}$$ .
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