Existence, uniqueness and regularity of the free boundary in the Hele-Shaw problem with a degenerate phase | Zendy

Ivan Blank | Zendy; M. Korten | Zendy; Charles N. Moore | Zendy

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Existence, uniqueness and regularity of the free boundary in the Hele-Shaw problem with a degenerate phase

Author(s) -

Ivan Blank,

M. Korten,

Charles N. Moore

Publication year - 2007

Publication title -

contemporary mathematics - american mathematical society

Language(s) - English

Resource type - Reports

SCImago Journal Rank - 0.106

H-Index - 12

eISSN - 1098-3627

pISSN - 0271-4132

DOI - 10.1090/conm/428/08208

Subject(s) - uniqueness , mathematics , degenerate energy levels , boundary (topology) , hele shaw flow , boundary problem , free boundary problem , phase (matter) , mathematical analysis , pure mathematics , flow (mathematics) , geometry , physics , open channel flow , quantum mechanics

The Hele-Shaw model describes the flow of a viscous fluid being injected into a slot between two nearby plates. It is used in injection molding for the production of packaging materials and the interior plastic parts of cars and airplanes, in electromechanical machining, and to study the diffusion of nutrients and medicines within certain tumors. We obtain the unique weak solution to the Hele-Shaw problem with a mushy zone as the (pointwise) “Mesa” type limit of solutions to one-phase Stefan problems with increasing diffusivities, and fixed initial and boundary data and discuss results on the regularity of the free boundary in space.

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