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

Abstract

We are interested in the convergence of a system of integrodifferential equations with respect to an asymptotic parameter $𝜀$. It appears in the context of cell adhesion modeling [Oelz and Schmeiser 2010; Oelz, Schmeiser and Small 2008]. We extend the framework from [Milišić and Oelz 2011; 2015], strongly depending on the hypothesis that the external load $f$ is in $\text{Lip}([0,T])$ to the case where $f\in \text{BV}(0,T)$ only. We show how results presented in [Milišić and Oelz 2015] naturally extend to this new setting, while only partial results can be obtained following the comparison principle introduced in [Milišić and Oelz 2011].