Anomalous diffusion in polymers: long-time behaviour

TL;DR

This paper investigates the long-term behavior of viscoelastic diffusion in polymers by analyzing the associated boundary value problem, demonstrating the existence of attractors that describe the system's asymptotic dynamics.

Contribution

It constructs the minimal trajectory attractor and the global attractor for the viscoelastic diffusion problem in polymers, advancing understanding of its long-time behavior.

Findings

Existence of a dissipative semiflow for the problem

Construction of the minimal trajectory attractor

Construction of the global attractor

Abstract

We study the Dirichlet boundary value problem for viscoelastic diffusion in polymers. We show that its weak solutions generate a dissipative semiflow. We construct the minimal trajectory attractor and the global attractor for this problem.