Quasistatic limit of a dynamic viscoelastic model with memory

TL;DR

This paper investigates the behavior of solutions to a viscoelastic model with memory as the rate of change approaches zero, demonstrating convergence to a stationary solution through rescaling.

Contribution

It establishes the quasistatic limit for a dynamic viscoelastic model with memory, connecting dynamic solutions to stationary ones.

Findings

Rescaled solutions converge to stationary solutions as data change rate tends to zero.

Provides rigorous proof of the quasistatic limit in viscoelastic models with memory.

Bridges dynamic and stationary models in viscoelasticity.

Abstract

We study the behaviour of the solutions to a dynamic evolution problem for a viscoelastic model with long memory, when the rate of change of the data tends to zero. We prove that a suitably rescaled version of the solutions converges to the solution of the corresponding stationary problem.