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Attractors-repellers in the space of contours in the Stokes-Leibenson problem for Hele-Shaw flows. (English. Russian original) Zbl 1338.37128
J. Math. Sci., New York 189, No. 4, 568-581 (2013); translation from Probl. Mat. Anal. 69, 23-34 (2013).
Summary: It is shown that, in the space of quasicontours playing a role of free boundaries in the Stokes-Leibenson problem, there is a manifold of codimension 1 such that some points of this manifold are attractors in the case of sink and repellers in the case of source, whereas, on the contrary, other points are repellers in the case of sink and attractor in the case of source.
MSC:
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
76D27 Other free boundary flows; Hele-Shaw flows
35Q35 PDEs in connection with fluid mechanics
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