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

Dorothee Knees; Chiara Zanini

doi:10.3934/dcdss.2020332

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2021, Volume 14, Issue 1: 121-149. Doi: 10.3934/dcdss.2020332

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

Dorothee Knees^1, , and
Chiara Zanini^2,

1.
University of Kassel, Institute for Mathematics, Heinrich-Plett-Str. 40, 34132 Kassel, Germany
2.
Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

^* Corresponding author: Dorothee Knees
^* Corresponding author: Dorothee Knees

Dedicated to Alexander Mielke to the occasion of his 60th birthday

Received: August 31, 2019

Revised: October 31, 2019

Early access: April 2020

Published: January 2021

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Abstract

We study a rate-independent system with non-convex energy 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.

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Mathematics Subject Classification: Primary: 35R05, 49J40; Secondary: 74C05, 35Q74, 35D40, 49J45.

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