A geometric evolution problem

Bergwall, Andréas

doi:10.1090/qam/1878258

Author: Andréas Bergwall
Journal: Quart. Appl. Math. 60 (2002), 37-73
MSC: Primary 76D27; Secondary 35R35, 76A05
DOI: https://doi.org/10.1090/qam/1878258
MathSciNet review: MR1878258
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Abstract: A traditional approach to compression moulding of polymers involves the study of a generalized Hele-Shaw flow of a power-law fluid, and leads to the $p$-Poisson equation for the instantaneous pressure in the fluid. By studying the convex dual of an equivalent extremal problem, one may let the power-law index of the fluid tend to zero. The solution of the resulting extremal problem, referred to as the asymptotically dual problem, is known to have the property that the flow is always directed towards the closest point on the boundary.

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