On problems with solution-dependent load

In Continuum Physics, general balance problems between internal fluxes and external sources
are considered, mostly on some domain Ω called a material body. Typically, the fluxes are
determined by a wanted field – the solution or configuration of the body, possibly augmented
by derivatives or other suitable quantities specifying the state of the system. In order to
obtain a closed problem formulation, initial and boundary conditions need to be provided as
well. In this paper, we discuss some issues appearing in the case that the sources, e.g. forces
in a mechanical problem, are not known in advance, but related to the wanted configuration
in terms of values and/or derivatives of the solution. An analogy between thermodynamic
and mechanical problems is shown.