document: Nonlinear systems arising from nonisothermal , non-Newtonian Hele-Shaw flows in the presence of body forces and sources In this paper , we first give a formal derivation of several systems of equations for injection moulding . This is done starting from the basic equations for nonisothermal , non-Newtonian flows in a three-dimensional domain . We derive systems for both -LRB- T/sup 0 / , p/sup 0 / -RRB- and -LRB- T/sup 1 / , p/sup 1 / -RRB- in the presence of body forces and sources . We find that body forces and sources have a nonlinear effect on the systems . We also derive a nonlinear `` Darcy law '' . Our formulation includes not only the pressure gradient , but also body forces and sources , which play the role of a nonlinearity . Later , we prove the existence of weak solutions to certain boundary value problems and initial-boundary value problems associated with the resulting equations for -LRB- T/sup 0 / , p/sup 0 / -RRB- but in a more general mathematical setting
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