Communications in Mathematical Sciences

Volume 14 (2016)

Number 5

Tear-off versus global existence for a structured model of adhesion mediated by transient elastic linkages

Pages: 1353 – 1372



Vuk Milišić (Laboratoire Analyse, Géométrie & Applications (LAGA), Université Paris 13, France)

Dietmar Oelz (Courant Institute, New York University, New York, N.Y., U.S.A.)


We consider a microscopic non-linear model for friction mediated by transient elastic linkages introduced in our previous works. In the present study, we prove existence and uniqueness of a solution to the coupled system under weaker hypotheses. The theory we present covers the case where the off-rate of linkages is unbounded but increasing at most linearly with respect to the mechanical load.

The time of existence is typically bounded, culminating in tear-off where the moving binding site does not have any bonds with the substrate. However, under additional assumptions on the external force, we prove global in time existence of a solution that consequently stays attached to the substrate.


friction coefficient, protein linkages, cell adhesion, renewal equation, effect of chemical bonds, integral equation, Volterra kernel

2010 Mathematics Subject Classification

35B40, 35Q92, 45D05

Published 18 May 2016