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Existence of a solution to the \(n\) dimensional problem of thermoelastic contact. (English) Zbl 0765.73059

We consider the quasistatic problem of frictionless contact of a thermoelastic body with a rigid foundation. It models the evolution of temperature and displacement in an elastic body that is subject to external forces and heat sources and that may come in contact with a rigid foundation. It is modeled as a variational inequality in which the operator is neither monotone nor coercive. We prove the existence of a “strong-weak” solution to the problem, provided that the coefficient of thermal expansion is sufficiently small. Our method is based on a technical use of truncation and on compactness arguments.

MSC:

74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
35M10 PDEs of mixed type
74A15 Thermodynamics in solid mechanics
49J40 Variational inequalities
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References:

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