Comptes Rendus
no. 1
Functional analysis/Mathematical physics
Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions
[Le caractère bien posé et lʼapproximation dʼun problème dʼévolution des mesures de masse avec des conditions frontières sur le flux]

Présenté par : the Editorial Board

Joep Evers1 ; Sander C. Hille2 ; Adrian Muntean1
1 CASA – Centre for Analysis, Scientific computing and Applications, ICMS – Institute for Complex Molecular Systems, Eindhoven University of Technology, The Netherlands
2 Mathematical Institute, Leiden University, The Netherlands
Comptes Rendus. Mathématique, Volume 352 (2014) no. 1, pp. 51-54.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.11.012
Joep Evers 1 ; Sander C. Hille 2 ; Adrian Muntean 1

1 CASA – Centre for Analysis, Scientific computing and Applications, ICMS – Institute for Complex Molecular Systems, Eindhoven University of Technology, The Netherlands
2 Mathematical Institute, Leiden University, The Netherlands 
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     title = {Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions},
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Joep Evers; Sander C. Hille; Adrian Muntean. Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions. Comptes Rendus. Mathématique, Volume 352 (2014) no. 1, pp. 51-54. doi : 10.1016/j.crma.2013.11.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.11.012/

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