Linear Viscoelasticity

Abstract

A rich source for vector-valued Volterra equations is the continuum mechanics for materials with memory, i.e. the theory of viscoelastic materials. In this section the basic concepts of this theory are introduced and the resulting boundary value problems are formulated. The discussion of the involved material functions shows that the notion of creep functions introduced in Section 4 appears here naturally. The well-posedness of some special problems which lead to Volterra equations of scalar type will be discussed, but also the limits of this class of equations become apparent.