On Some Models for Elastic Solids with Micro-Structure

We review the concept of well-posedness in the context of evolutionary problems from mathematical physics for a particular subclass of problems from elasticity theory. The complexity of physical phenomena appears as encoded in so called material laws. The usefulness of the structural perspective developed is illustrated by showing that many initial boundary value problems in the theory of elastic solids share the same type of solution theory. Moreover, interconnections of the respective models are discussed via a previously introduced mother/descendant mechanism.