Communications in Mathematical Sciences
Volume 14 (2016)
Tear-off versus global existence for a structured model of adhesion mediated by transient elastic linkages
Pages: 1353 – 1372
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