J. R. Fernandez, K. L. Kuttler and M. Shillor

The existence of a weak solution to a model for the dynamic thermomechanical
behavior of a viscoelastic beam, which is in frictional contact with a rigid
rotating wheel, is established. The model describes a simple braking system
in which a rotating wheel comes to a stop as a result of the frictional
traction generated by the beam. The classical model consists of a system of
coupled equations for the beam's temperature and displacement, the wear of
the beam's contacting end, the wheel's temperature and its angular velocity.
The weak formulation is an abstract differential inclusion involving set-valued
pseudomonotone operators, The existence is proved by using recent results
for such operators. Uniqueness is shown to hold when the wheel's angular
velocity and temperature are known.