Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads

TL;DR

This paper establishes the existence of parameterized BV-solutions for rate-independent systems with discontinuous loads, using viscous regularization and vanishing viscosity techniques, and proves the compactness of the solution set.

Contribution

It introduces a novel approach to prove existence of BV-solutions for systems with discontinuous loads via viscous regularization and vanishing viscosity methods.

Findings

Existence of viscous regularization solutions for the system.

Existence of parameterized BV-solutions via vanishing viscosity.

Compactness of the solution set.

Abstract

We study a rate-independent system with non-convex energy and in the case of a time-discontinuous loading. We prove existence of the rate-dependent viscous regularization by time-incremental problems, while the existence of the so called parameterized $BV$-solutions is obtained via vanishing viscosity in a suitable parameterized setting. In addition, we prove that the solution set is compact.