Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange

In this paper, we study a nonlinear interaction problem between thermoelastic shell and heat-conducting fluid. The is governed by linear thermoelasticity equations encompasses time-dependent domain which filled with fluid the full Navier-Stokes-Fourier system. are fully coupled, giving rise to novel moving boundary fluid-structure involving heat exchange. existence of weak solution obtained combining three approximation techniques – decoupling, penalization extension. particular, extension allow us use methods already developed for compressible fluids on domains. such way, proof more elegant analysis drastically simplified. Let stress that first time exchange in context problems considered.