We establish some decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation u t (t)−βΔu(t)−∫ 0 ∞ k(s)Δu(t−s) ds=0 describing hereditary heat conduction.
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Chepyzhov et al. (2006) studied this question.
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