Hele-Shaw flows with time-dependent free boundaries involving an infinite strip of fluid

Richardson, S.

doi:10.1090/qam/1686185

Author: S. Richardson
Journal: Quart. Appl. Math. 57 (1999), 201-212
MSC: Primary 76D27; Secondary 35Q35, 76S05
DOI: https://doi.org/10.1090/qam/1686185
MathSciNet review: MR1686185
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Abstract: We present a new family of analytic solutions for Hele-Shaw flows with time-dependent free boundaries, a constant-pressure condition being supposed relevant on each free boundary. The basic starting configuration has the plan-view of the region occupied by fluid within the Hele-Shaw cell as an infinite strip bounded by parallel lines, these lines being the free boundaries. The subsequent motion is produced by the injection (or suction) of fluid at points within the strip and, perhaps, the imposition of a pressure difference between the two boundaries.

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