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Analysis of a class of thermal frictional contact problem
for the Norton-Hoff fluid
Received: March 7, 2009; Revised: October 4, 2010; Accepted: April 7, 2011
Abstract. We consider a mathematical model which describes the static flow of a Norton-Hoff fluid whose viscosity depends on the temperature, and with mixed boundary conditions, including friction. The latter is modelled by a general velocity dependent dissipation functional and the temperature. We derive a weak formulation of the coupled system of the equation of motion and the energy equation, consisting of a variational inequality for the velocity field. We prove the existence of a weak solution of the model using compactness, monotonicity, L1-data theory and a fixed point argument. In the asymptotic limit case of a high thermal conductivity, the temperature becomes a constant solving an implicit total energy equation involving the viscosity function and the subdifferential friction. Finally, we describe a number of concrete thermal friction conditions.
Keywords: Frictional contact; Norton-Hoff fluid; subdifferential; thermal conductivity; variational inequality.
AMS Subject classification: Primary: 35J85 Secondary: 76D03, 80A20
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