Analysis of a quasi-variational contact problem arising in thermoelasticity

We formulate and study two mathematical models of a thermoforming process involving membrane mould as implicit obstacle problems. In particular, the membrane-mould coupling is determined by thermal displacement that depends in turn on through contact region. The considered are stationary (or elliptic) model an evolutionary quasistatic) one. For first model, we prove existence weak solutions solving elliptic quasi-variational inequality coupled to equations. By exploring fine properties variation set under non-degenerate data, give sufficient conditions for regular solutions, certain contraction conditions, also uniqueness result. apply these results series semi-discretised problems arise approximations or quasistatic problem. Here, able problem special case, time-dependent solutions.