  We consider a microscopic model for friction mediated by transient elastic
linkages introduced in [V. Milisic and D. Oelz. SIAM J. on Math. Anal. (2015).
V. Milisic and D. Oelz. J. Math. Pures Appl. (2011)]. 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 and corresponds to 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.
