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- W2103394312 abstract "Short-time existence and uniqueness results in Sobolev spaces are proved for Hele-Shaw flow with kinetic undercooling and for Stokes flow without surface tension. In both cases, the flow is driven by arbitrarily distributed sources and sinks in the interior of the liquid domain. The proofs are based on a general approach consisting of the reformulation of the problem as a Cauchy problem for a nonlinear, nonlocal evolution equation on the unit sphere, quasilinearization by equivariance, investigation of the linearization, and Galerkin approximations. In the situation discussed here, the linearized evolution operator is a first-order differential operator, and thus the evolution equation is of hyperbolic type. Finally, a brief survey of the properties of the evolution equations that arise from Hele-Shaw flow and Stokes flow with and without regularization is given." @default.
- W2103394312 created "2016-06-24" @default.
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- W2103394312 date "1999-12-01" @default.
- W2103394312 modified "2023-09-26" @default.
- W2103394312 title "Hyperbolic evolution equations for moving boundary problems" @default.
- W2103394312 doi "https://doi.org/10.1017/s0956792599003836" @default.
- W2103394312 hasPublicationYear "1999" @default.
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