We establish a necessary and sufficient conditionof exponential stability for the contraction semigroup generatedby an abstract version of the linear differential equation∂ₜ u(t)-∫₀^∞ k(s)Δ u(t-s)ds = 0modeling hereditary heat conduction of Gurtin-Pipkin type.
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Conti et al. (2013) studied this question.
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