Abstract
The solvability of a coupled thermoviscoelastic contact problem with Coulomb friction is investigated. The heat generated by friction is described by a boundary term of quadratic order. The tensor of thermal conductivity is dependent on the temperature gradient and satisfies a certain growth condition.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Duvaut, G. and Lions, J.L. (1972). Les inéquations en mécanique et en physique. Dunod, Paris.
Eck, C. (1996). Existenz und Regularität der Lösungen für Kontaktprobleme mit Reibung. PhD-Thesis, University of Stuttgart.
Eck, C. and Jarušek, J. (1998). The solvability of a coupled thermoviscoelastic contact problem with small Coulomb friction and linearized growth of frictional heat. SFB 404, Preprint 98/04, University of Stuttgart. To appear in Math. Meth. Appl. Sci.
Eck, C. and Jarušek, J. (1998). Existence of solutions for the dynamic frictional contact problem of isotropic elastic bodies. Preprint No. 242, Institute for Applied Mathematics, University Erlangen-Nürnberg.
Jarušek, J. and Eck, C. (1996). Dynamic contact problems with friction in linear viscoelasticity. C. R. Acad. Sci. Paris, Sir. I, 322:507–512.
Jarušek, J. and Eck, C. (1999). Dynamic contact problems with small Coulomb friction for viscoelastic bodies. Existence of solutions. Math. Models & Meth. Appl. Sci., 9(l):11–34.
Lions, J.L. and Magenes, E. (1968). Problèmes aux limites non-homogènes et applications. Dunod, Paris.
Nečas, J. (1989). Dynamics of thermoelastic systems with strong viscosity. In: Proc. confer, partial diff. eq., 25.–29.3.1988, Holzhau, GDR. Teubner Texte Math., Leipzig.
Nečas J., Jarušek, J. and J. Haslinger. (1980). On the solution of the variational inequality to the Signorini problem with small friction. Boll. Un. Mat. Ital., 5(17–B):796–811.
Nečas J., Novotný, A. and Šverák, V. (1990). Uniqueness of solutions to the system of thermoelastic bodies with strong viscosity. Math. Nachr., 150:319–324.
Nečas J. and Růžička, M. (1991). A dynamic problem of thermoelasticity. Z. Anal. Anwendungen, 10(3):358–368.
Nečas J. (1967). Les méthodes directes en équations elliptiques. Academia, Praha.
Sprekels, J. (1991). Global solutions in onedimensional magneto-thermo-viscoelasticity. European J. Appl. Math., 2:83–96.
Triebel, H. (1978). Interpolation Theory, Function Spaces, Differential Operators. North Holland, Amsterdam — New York — Oxford.
Zeidler, E. (1990). Nonlinear Functional Analysis and its Applications. II B: Monotone Operators, Springer-Verlag, New York.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Kluwer Academic Publishers
About this chapter
Cite this chapter
Eck, C., Jarušek, J. (2002). Existence of Solutions to a Nonlinear Coupled Thermo-Viscoelastic Contact Problem with Small Coulomb Friction. In: Sequeira, A., da Veiga, H.B., Videman, J.H. (eds) Applied Nonlinear Analysis. Springer, Boston, MA. https://doi.org/10.1007/0-306-47096-9_5
Download citation
DOI: https://doi.org/10.1007/0-306-47096-9_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-306-46303-7
Online ISBN: 978-0-306-47096-7
eBook Packages: Springer Book Archive