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.
Mots clés : concentrations, energetic solution, energies with linear growth, oscillations, relaxation
@article{COCV_2010__16_1_1_0,
author = {Kru\v{z}{\'\i}k, Martin and Zimmer, Johannes},
title = {Evolutionary problems in non-reflexive spaces},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1--22},
publisher = {EDP-Sciences},
volume = {16},
number = {1},
year = {2010},
doi = {10.1051/cocv:2008060},
mrnumber = {2598085},
zbl = {1183.49015},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2008060/}
}
TY - JOUR AU - Kružík, Martin AU - Zimmer, Johannes TI - Evolutionary problems in non-reflexive spaces JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 1 EP - 22 VL - 16 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2008060/ DO - 10.1051/cocv:2008060 LA - en ID - COCV_2010__16_1_1_0 ER -
%0 Journal Article %A Kružík, Martin %A Zimmer, Johannes %T Evolutionary problems in non-reflexive spaces %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 1-22 %V 16 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2008060/ %R 10.1051/cocv:2008060 %G en %F COCV_2010__16_1_1_0
Kružík, Martin; Zimmer, Johannes. Evolutionary problems in non-reflexive spaces. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 1, pp. 1-22. doi : 10.1051/cocv:2008060. http://www.numdam.org/articles/10.1051/cocv:2008060/
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