Friction mediated by transient elastic linkages: extension to loads of bounded variation

Abstract

In this work, we are interested in the convergence of a system of integro-differential equations with respect to an asymptotic parameter ε. It appears in the context of cell adhesion modelling [16, 15]. We extend the framework from [12, 13], strongly depending on the hypothesis that the external load f is in Lip([0, T ]) to the case where f ∈ BV(0, T ) only. We show how results presented in [13] naturally extend to this new setting, while only partial results can be obtained following the comparison principle introduced in [12].