Wave hierarchies in viscoelasticity

TL;DR

This paper analyzes a family of evolution operators in viscoelasticity, deriving explicit solutions and asymptotic properties, with applications to polymer chain models like Rouse and reptation.

Contribution

It introduces a generalized operator framework for viscoelastic models and explicitly derives fundamental solutions, extending known results to arbitrary n.

Findings

Explicit fundamental solutions for L_n are obtained.

Asymptotic properties and maximum theorems are established.

Applications to polymer models like Rouse and reptation are demonstrated.

Abstract

An evolution operator L_n 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 {\epsilon}n of L_n is explicitly obtained and it's estimated in terms of the fundamental solution {\epsilon}1 of L_1. 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.