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A dynamic contact problem in one-dimensional thermoviscoelasticity. (English) Zbl 0831.73054

Summary: The problem of dynamic contact or impact of a one-dimensional thermoviscoelastic rod, of the Kelvin-Voigt type, with a rigid obstacle is shown to possess a weak solution. The thermal interaction between the rod and the obstacle is modeled by a graph that depends on the distance between the free end and the wall. The contact is modeled by Signorini’s condition. The problem consists of a parabolic partial differential equation for the temperature, coupled with a variational inequality for the displacement. The existence of a weak solution is established by considering penalized and time-retarded approximations. Possible steady solutions are discussed briefly.

MSC:

74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74M20 Impact in solid mechanics
74Hxx Dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
80A20 Heat and mass transfer, heat flow (MSC2010)
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