Evolutionary problems in non-reflexive spaces

Martin Kružík; Johannes Zimmer

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 1, page 1-22
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Kružík, Martin, and Zimmer, Johannes. "Evolutionary problems in non-reflexive spaces." ESAIM: Control, Optimisation and Calculus of Variations 16.1 (2010): 1-22. <http://eudml.org/doc/250727>.

@article{Kružík2010,
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. },
author = {Kružík, Martin, Zimmer, Johannes},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Concentrations; energetic solution; energies with linear growth; oscillations; relaxation; concentrations; energies with linear growth},
language = {eng},
month = {1},
number = {1},
pages = {1-22},
publisher = {EDP Sciences},
title = {Evolutionary problems in non-reflexive spaces},
url = {http://eudml.org/doc/250727},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Kružík, Martin
AU - Zimmer, Johannes
TI - Evolutionary problems in non-reflexive spaces
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/1//
PB - EDP Sciences
VL - 16
IS - 1
SP - 1
EP - 22
AB - 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.
LA - eng
KW - Concentrations; energetic solution; energies with linear growth; oscillations; relaxation; concentrations; energies with linear growth
UR - http://eudml.org/doc/250727
ER -

References

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