Vol. LXXX, 2 (2012)
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, 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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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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Comenius University
842 48 Bratislava, Slovak Republic  

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