Rate-independent processes with linear growth energies and   time-dependent boundary conditions

Martin Kružík; Johannes Zimmer

doi:10.3934/dcdss.2012.5.591

Article Contents

2012, Volume 5, Issue 3: 591-604. Doi: 10.3934/dcdss.2012.5.591

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Rate-independent processes with linear growth energies and time-dependent boundary conditions

Martin Kružík^1, and
Johannes Zimmer^2,

1.
Institute of Information Theory and Automation of the ASCR, Pod vodárenskou věží 4, CZ-182 08 Praha 8
2.
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY

Received: July 31, 2010

Revised: December 31, 2010

Published: May 2012

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Abstract

A rate-independent evolution problem is considered for which the stored energy density depends on the gradient of the displacement. The stored energy density does not have to be quasiconvex and is assumed to exhibit linear growth at infinity; no further assumptions are made on the behaviour at infinity. We analyse an evolutionary process with positively $1$-homogeneous dissipation and time-dependent Dirichlet boundary conditions.

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Mathematics Subject Classification: Primary: 74C15; Secondary: 49J45, 74G65.

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