K. L. Kuttler and M. Shillor

Abstract. The regularity in time of solutions to a problem of frictionless
dynamic contact between a viscoelastic body and a reactive foundation is
established. Contact is modelled with the normal compliance condition. It is
shown that the differentiability of the normal compliance function, its behavior
at the onset of contact, determinesthe regularity of the solution, and additional
differentiability of the dataand appropriate compatibility on the initial conditions
yield higher solutions' differentiability. Unlike the case when the Signorini condition
is used, in this problem there is no intrinsic regularity ceiling. A simple example
shows that these results are close to being optimal.