Reliable solution of an unilateral contact problem with friction and uncertain data in thermo-elasticity

An unilateral contact problem with friction and with uncertain input data in quasi-coupled thermo-elasticity is analysed. As uncertain data coefficients of stress–strain law, coefficients of thermal conductivity, body and surface forces, thermal sources and friction coefficients are assumed, being prescribed in a given set of admissible functions. Method of worst scenario is applied to find the most “dangerous” admissible input data. Stability of the solution with respect to the data is proved and employed for the proof of existence of a solution to the worst scenario problems. Some models in geomechanics, geodynamics and mechanics as well as in technology are stated and the safety of the high level radioactive waste repositories is considered.