Thermoelastic contact problems can posess non-unique and/or unstable steady-state solutions if there is frictional heating or if there is a pressure-dependent thermal contact resistance at the interface. These two effects have been extensively studied in isolation, but their possible interaction has not been investigated until recently. We shall discuss some idealized geometries in which the two effects are seen to form limiting cases of a more general stability and existence behavior. In most cases, frictional heating has a destabilizing effect relative to the static contact problem, but if the thermal contact resistance is very sensitive to pressure, cases of stabilization can be obtained. Also, the critical sliding speed depends on the contact pressure in contrast to results obtained in the absence of thermal contact resistance.

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