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On a two-phase Hele-Shaw problem with a time-dependent gap and distributions of sinks and sources. (arXiv:1711.02533v1 [math.AP])
来源于:arXiv
A two-phase Hele-Show problem with a time-dependent gap describes the
evolution of the interface, which separates two fluids sandwiched between two
plates. The fluids have different viscosities. In addition to the change in the
gap width of the Hele-Shaw cell, the interface is driven by the presence of
some special distributions of sinks and sources located in both the interior
and exterior domains. The effect of surface tension is neglected. Using the
Schwarz function approach, we give examples of exact solutions when the
interface belongs to a certain family of algebraic curves and the curves do not
form cusps. The family of curves are defined by the initial shape of the free
boundary. 查看全文>>