Existence for a thermoviscoelastic beam model of brakes

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 temperature and displacement, the wear of the beam's contacting end, the wheel 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.

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