Geodesic
Initial Layer Analysis for a Linkage Density in Cell Adhesion Mechanisms
Vuk Milisic1
1Laboratoire Analyse & Géométrie, Université Villeteuse Paris 13, France
ESAIM. Proceedings, Tome 62 (2018), pp. 108-122
Cet article a éte moissonné depuis la source EDP Sciences

Voir la notice de l'article

In this paper we present a non local age structured equation involved in cell motility modeling [5, 9, 11]. It describes the evolution of a density of linkages of a point submitted to adhesion. It depends on an asymptotic parameter ɛ representing the characteristic age of linkages. Here we introduce a new initial layer term in the asymptotic expansion with respect to ɛ. This improves error estimates obtained in [5]. Moreover, we study the convergence of the time derivative of this density and show how a singular term appears when ɛ goes to zero. We show convergence, in the tight topology of measures, to the time derivative of the limit solution and a Dirac mass supported on the initial half-axis. In order to illustrate these results, numerical simulations are performed and compared to the asymptotic expansion for various values of ɛ.
DOI : 10.1051/proc/201862108

Vuk Milisic  1

1 Laboratoire Analyse & Géométrie, Université Villeteuse Paris 13, France 
@article{EP_2018_62_a9,
     author = {Vuk Milisic},
     title = {Initial {Layer} {Analysis} for a {Linkage} {Density} in {Cell} {Adhesion} {Mechanisms}},
     journal = {ESAIM. Proceedings},
     pages = {108--122},
     year = {2018},
     volume = {62},
     doi = {10.1051/proc/201862108},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201862108/}
}
TY  - JOUR
AU  - Vuk Milisic
TI  - Initial Layer Analysis for a Linkage Density in Cell Adhesion Mechanisms
JO  - ESAIM. Proceedings
PY  - 2018
SP  - 108
EP  - 122
VL  - 62
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc/201862108/
DO  - 10.1051/proc/201862108
LA  - en
ID  - EP_2018_62_a9
ER  - 
%0 Journal Article
%A Vuk Milisic
%T Initial Layer Analysis for a Linkage Density in Cell Adhesion Mechanisms
%J ESAIM. Proceedings
%D 2018
%P 108-122
%V 62
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201862108/
%R 10.1051/proc/201862108
%G en
%F EP_2018_62_a9
Vuk Milisic. Initial Layer Analysis for a Linkage Density in Cell Adhesion Mechanisms. ESAIM. Proceedings, Tome 62 (2018), pp. 108-122. doi: 10.1051/proc/201862108

Cité par Sources :