We discuss a novel approach to the mathematical analysis of equations with memory, based on the notion of a {\it state}. This is the initial configuration of the system at time t=0 which can be unambiguously determined by the knowledge of the dynamics for positive times. As a model, for a nonincreasing convex function G:R^->R^+ such that G(0) = lim_{s->0} G(s) > lim_{s->infty} G(s)>0 we consider an abstract version of the evolution equation u_{tt} -\Delta [G(0)u +\int_0^\infty G'(s)u(t-s)ds]=0 arising from linear viscoelasticity.

### A new approach to equations with memory

#### Abstract

We discuss a novel approach to the mathematical analysis of equations with memory, based on the notion of a {\it state}. This is the initial configuration of the system at time t=0 which can be unambiguously determined by the knowledge of the dynamics for positive times. As a model, for a nonincreasing convex function G:R^->R^+ such that G(0) = lim_{s->0} G(s) > lim_{s->infty} G(s)>0 we consider an abstract version of the evolution equation u_{tt} -\Delta [G(0)u +\int_0^\infty G'(s)u(t-s)ds]=0 arising from linear viscoelasticity.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/580563