J. Bajkowski, K. L. Kuttler and M. Shillor

A model for the dynamic thermomechanical behavior of a viscoelastic beam
which is in frictional contact with a rigid rotating wheel is presented. It
describes a simple braking system in which the wheel comes to a stop as a
result of the frictional traction generated by the beam. Friction is modeled
by a version of the Coulomb law, with a temperature and slip rate dependent
coefficient of friction. Frictional heat generation is taken into account as
well as the wheel's temperature evolution, and the wear of the contacting
end. The model is formulated as a differential inclusion involving set
valued pseudomonotone operators, and the existence of a weak solution is
established. Uniqueness is shown to hold when the wheel's angular velocity
and temperature are known.