p. 143 - 160 Analysis of a class of thermal frictional contact problem
for the Norton-Hoff fluid F. Messelmi 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, L^{1}-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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