Existence of long-time solutions to dynamic problems of viscoelasticity with rate-and-state friction

TL;DR

This paper proves the existence of long-term solutions for a dynamic contact problem involving a viscoelastic body and rate-and-state friction, relevant to geosciences.

Contribution

It establishes the existence of solutions for a complex viscoelastic contact problem with rate-and-state friction laws, including the ageing law.

Findings

Proves existence of long-time solutions.

Applicable to rate-and-state friction laws used in geosciences.

Addresses dynamic contact problems with viscoelastic materials.

Abstract

We establish existence of long-time solutions to a dynamic problem of bilateral contact between a rigid surface and a viscoelastic body, subject to rate-and-state friction. The term rate-and-state friction is used here to refer to a set of functions and equations satisfying conditions which rule out the slip law but do cover the ageing law, and thus at least one of the rate-and-state friction laws commonly used in the geosciences.