scholarly journals Relaxation limit and initial layer analysis of a bipolar hydrodynamic model for semiconductors

2009 ◽  
Vol 50 (3-4) ◽  
pp. 470-480 ◽  
Author(s):  
Yeping Li
Keyword(s):  
Hydrodynamic Model ◽  
Initial Layer ◽  
Layer Analysis ◽  
Bipolar Hydrodynamic Model

scholarly journals Initial Layer Analysis for a Linkage Density in Cell Adhesion Mechanisms

2018 ◽  
Vol 62 ◽  
pp. 108-122 ◽  
Author(s):  
Vuk Milisic
Keyword(s):  
Asymptotic Expansion ◽  
Singular Term ◽  
Time Derivative ◽  
Initial Layer ◽  
Limit Solution ◽  
Layer Analysis ◽  
Non Local ◽  
Asymptotic Parameter ◽  
Age Structured ◽  
Half Axis

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.

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