[Le caractère bien posé et lʼapproximation dʼun problème dʼévolution des mesures de masse avec des conditions frontières sur le flux]
Dans cette Note, nous étudions lʼévolution de mesures (de masse) dans un intervalle borné où la dynamique non conservative est imposée à lʼaide de conditions frontières de type flux. Nous montrons le caractère bien posé du problème en exploitant des systèmes de particules et lʼaccumulation de masse provoquée par ces particules dans une couche limite tout près de la frontière active. Finalement, nous obtenons la vitesse de convergence de la procedure dʼapproximation ainsi que la structure de la condition de frontière concernant le problème limite.
This Note deals with imposing a flux boundary condition on a non-conservative measure-valued mass evolution problem posed on a bounded interval. To establish the well-posedness of the problem, we exploit particle system approximations of the mass accumulation in a thin layer near the active boundary. We derive the convergence rate for the approximation procedure as well as the structure of the flux boundary condition in the limit problem.
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@article{CRMATH_2014__352_1_51_0,
author = {Evers, Joep and Hille, Sander C. and Muntean, Adrian},
title = {Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions},
journal = {Comptes Rendus. Math\'ematique},
pages = {51--54},
publisher = {Elsevier},
volume = {352},
number = {1},
year = {2014},
doi = {10.1016/j.crma.2013.11.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2013.11.012/}
}
TY - JOUR AU - Evers, Joep AU - Hille, Sander C. AU - Muntean, Adrian TI - Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions JO - Comptes Rendus. Mathématique PY - 2014 SP - 51 EP - 54 VL - 352 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.11.012/ DO - 10.1016/j.crma.2013.11.012 LA - en ID - CRMATH_2014__352_1_51_0 ER -
%0 Journal Article %A Evers, Joep %A Hille, Sander C. %A Muntean, Adrian %T Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions %J Comptes Rendus. Mathématique %D 2014 %P 51-54 %V 352 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.11.012/ %R 10.1016/j.crma.2013.11.012 %G en %F CRMATH_2014__352_1_51_0
Evers, Joep; Hille, Sander C.; Muntean, Adrian. Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions. Comptes Rendus. Mathématique, Tome 352 (2014) no. 1, pp. 51-54. doi : 10.1016/j.crma.2013.11.012. http://www.numdam.org/articles/10.1016/j.crma.2013.11.012/
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