Viscoelasticity and Electrodynamics with Memory

Abstract

The discussion of problems in linear viscoelasticity leading to linear abstract Volterra equations which was begun in Section 5 is continued here. Models for viscoelastic beams and plates are introduced and their well-posedness is studied by means of the results on Volterra equations of scalar type from Chapter I but also by those on equations of nonscalar type from this chapter. In Sections 9.3 and 9.4 two approaches to general linear thermoviscoelasticity based on the results of Sections 6, 7, and 8 are carried through. Under physically reasonable assumptions these yield well-posedness in the variational setting, but also in the strong if the material in question is almost separable. In Sections 9.5 and 9.6 memory effects in isotropic linear electrodynamics are discussed and via the perturbation method well-posedness of the whole space problem as well as of a transmission problem are proved.