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

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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 
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     author = {Vuk Milisic},
     title = {Initial {Layer} {Analysis} for a {Linkage} {Density} in {Cell} {Adhesion} {Mechanisms}},
     journal = {ESAIM. Proceedings},
     pages = {108--122},
     publisher = {mathdoc},
     volume = {62},
     year = {2018},
     doi = {10.1051/proc/201862108},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201862108/}
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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. http://geodesic.mathdoc.fr/articles/10.1051/proc/201862108/

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