Nonlinear systems arising from nonisothermal, non-Newtonian Hele-Shaw flows in the presence of body forces and sources

Authors:
R. P. Gilbert;M. Fang
Affiliations:
Department of Mathematical Science University of Delaware, Newark, DE 19716, U.S.A.;Department of Mathematical Science University of Delaware, Newark, DE 19716, U.S.A.
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2002

Citing 1
Cited 2

Nonisothermal, nonNewtonian Hele-Shaw flows, part II: asymptotics and existence of weak solutions

Nonlinear Analysis: Theory, Methods & Applications

Thermally coupled quasi-Newtonian flows: Analysis and computation

Journal of Computational and Applied Mathematics
Non-isothermal, non-Newtonian Hele-Shaw flows within Cattaneo's heat flux law

Mathematical and Computer Modelling: An International Journal

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Abstract

In this paper, we 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 (T^0, p^0) and (T^1, p^1) 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 (T^0,p^0) but in a more general mathematical setting.