Wave hierarchies in viscoelasticity

An evolution operator ℳn with n arbitrary, typical of several models, is analyzed. When n = 1, the operator characterizes the standard linear solid of viscoelasticity, whose properties are already established in previous papers. The fundamental solution εn of ℳn is explicitly obtained and itʹs estimated in terms of the fundamental solution ε1 of ℳ1. So, whatever n may be, asymptotic properties and maximum theorems are achieved. These results are applied to the Rouse model and reptation model, which describe different aspects of polymer chains.