Geodesic
General solution of the one-phase Hele-Shaw problem for elliptic bubble
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 80-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the general case of several multipole we study one-phase Hele-Shaw flow with a moving boundary when surface tension effect is negligible. We find the explicit solution with nonstationary elliptic shape of the bubble for case when Hele-Shaw flow is produced by any combination of sink, dipole and quadropole at infinity. This general solution includes all known particular cases. In the particular case of a dipole at infinity we find new explicit solution with stationary elliptic shape of the bubble that is not symmetrical with respect to the flow.
Keywords: one-phase Hele-Shaw problem, elliptic bubble. 
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M. M. Alimov. General solution of the one-phase Hele-Shaw problem for elliptic bubble. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 80-92. http://geodesic.mathdoc.fr/item/UZKU_2010_152_1_a7/

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