Stability of abstract linear semigroups arising from heat conduction with memory

Abstract

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.