Stability and exponential stability in linear viscoelasticity

摘要

In this survey paper, we discuss the decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation $${partial_{tt}}u(t) - Delta u(t) + {int_0^infty} mu(s) Delta u(t - s) {rm{d}}s = 0$$ describing the dynamics of linearly viscoelastic bodies.