We are interested in the existence results for second-order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal normal cone to a time-dependent set. In order to prove these existence results, we study an extension of the numerical scheme introduced in [10] and prove a convergence result for this scheme.
@article{CML_2010__2_4_445_0,
author = {Bernicot, Fr\'ed\'eric and Lefebvre-Lepot, Aline},
title = {Existence results for nonsmooth second-order differential inclusions, convergence result for a numerical scheme and application to the modeling of inelastic collisions},
journal = {Confluentes Mathematici},
pages = {445--471},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {2},
number = {4},
year = {2010},
doi = {10.1142/S1793744210000247},
language = {en},
url = {http://www.numdam.org/articles/10.1142/S1793744210000247/}
}
TY - JOUR AU - Bernicot, Frédéric AU - Lefebvre-Lepot, Aline TI - Existence results for nonsmooth second-order differential inclusions, convergence result for a numerical scheme and application to the modeling of inelastic collisions JO - Confluentes Mathematici PY - 2010 SP - 445 EP - 471 VL - 2 IS - 4 PB - World Scientific Publishing Co Pte Ltd UR - http://www.numdam.org/articles/10.1142/S1793744210000247/ DO - 10.1142/S1793744210000247 LA - en ID - CML_2010__2_4_445_0 ER -
%0 Journal Article %A Bernicot, Frédéric %A Lefebvre-Lepot, Aline %T Existence results for nonsmooth second-order differential inclusions, convergence result for a numerical scheme and application to the modeling of inelastic collisions %J Confluentes Mathematici %D 2010 %P 445-471 %V 2 %N 4 %I World Scientific Publishing Co Pte Ltd %U http://www.numdam.org/articles/10.1142/S1793744210000247/ %R 10.1142/S1793744210000247 %G en %F CML_2010__2_4_445_0
Bernicot, Frédéric; Lefebvre-Lepot, Aline. Existence results for nonsmooth second-order differential inclusions, convergence result for a numerical scheme and application to the modeling of inelastic collisions. Confluentes Mathematici, Tome 2 (2010) no. 4, pp. 445-471. doi : 10.1142/S1793744210000247. http://www.numdam.org/articles/10.1142/S1793744210000247/
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