ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE




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



PDF                               Compressed Postscript                                 Version to read






Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

Telephone: + 421-2-60295111 Fax: + 421-2-65425882  
e-Mail: amuc@fmph.uniba.sk    Internet: www.iam.fmph.uniba.sk/amuc
© 2011, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE