Initial Layer Analysis for a Linkage Density in Cell Adhesion Mechanisms★

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.

Abstract licence: CC BY-NC

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