Nonlinear systems arising from nonisothermal, non-Newtonian Hele-Shaw flows in the presence of body forces and sources |
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Authors: | R P Gilbert M Fang |
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Institution: | Department of Mathematical Science University of Delaware, Newark, DE 19716, U.S.A. |
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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 (T0, p0) and (T1, p1) 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 (T0,p0) but in a more general mathematical setting. |
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Keywords: | Nonlinear systems Darcy law Asymptotic analysis Fixed-point methods Weak solutions |
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