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Evolutionary problems in non-reflexive spaces

Published online by Cambridge University Press:  21 October 2008

Martin Kružík  and
Johannes Zimmer
Martin Kružík
Affiliation:
Corresponding address: Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 4, 182 08 Praha 8, Czech Republic. Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 166  29 Praha 6, Czech Republic. kruzik@utia.cas.cz
Johannes Zimmer
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. zimmer@maths.bath.ac.uk
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Abstract

Rate-independent problems are considered, where the stored energy density is a function of the gradient. The stored energy density may not be quasiconvex and is assumed to grow linearly. Moreover, arbitrary behaviour at infinity is allowed. In particular, the stored energy density is not required to coincide at infinity with a positively 1-homogeneous function. The existence of a rate-independent process is shown in the so-called energetic formulation.

Keywords

Concentrationsenergetic solutionenergies with linear growthoscillationsrelaxation
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 1 , January 2010 , pp. 1 - 22
Copyright
© EDP Sciences, SMAI, 2008

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