Hele-Shaw Flows: Historical Overview

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Free Boundary Problem • ∆p = Qδ0(z), for z ∈ Ω(t); • p = 0, where Γ(t) = ∂Ω(t); • ∂p ∂n z∈Γ(t) z∈Γ(t) = −v n . Q < 0 for injection, Q > 0 for sucction. In the case of surface tension replace 0 by βκ(z,t) where β is surface tension, κ is the mean curvature. BIRS, Canada, July 2007 – p. 37
P. Ya. Polubarinova-Kochina Pelageya Yakovlevna Polubarinova-Kochina (13 May 1899–3 July 1999). One of the most important women in mathematics in the Soviet Union and one of its leading scientists. BIRS, Canada, July 2007 – p. 38
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Hele-Shaw Flows: Historical Overvie
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Henri Selby Hele-Shaw ... an exampl
Page 5 and 6:
1871-1876 At the age of 17 he finis
Page 7 and 8: 1885-1904 In 1885 Hele-Shaw was inv
Page 9 and 10: 1906-1941 Upon returning from South
Page 11 and 12: 1906-1941 Upon returning from South
Page 13 and 14: 1906-1941 Hele-Shaw took a very act
Page 19 and 20: 1906-1941 One of his greatest contr
Page 21 and 22: 1906-1941 Hele-Shaw was a man of gr
Page 23 and 24: 1906-1941 Hele-Shaw was a man of gr
Page 25 and 26: Hele-Shaw’s inventions Two greate
Page 27 and 28: Hele-Shaw’s inventions • Specia
Page 29 and 30: Hele-Shaw’s inventions H. S. Hele
Page 31 and 32: Hele-Shaw’s inventions Further de
Page 33 and 34: Hele-Shaw Prizes • Hele-Shaw Priz
Page 35 and 36: Stream-line Flow Methods The most n
Page 37 and 38: Stream-line Flow Methods In 1897 He
Page 39 and 40: Experiment by Reynolds O. Reynolds
Page 41 and 42: Experiment by Reynolds O. Reynolds
Page 43 and 44: Hele-Shaw Cell Hele-Shaw got the Go
Page 45 and 46: Hele-Shaw Papers • Experiments on
Page 47 and 48: USSR CONTRIBUTION BIRS, Canada, Jul
Page 49 and 50: Stokes-Leibenzon Model Leonid Samui
Page 51 and 52: Stokes-Leibenzon Model x3 h 0 x1,x3
Page 53 and 54: Stokes-Leibenzon Model Ω(t) 0 y
Page 55 and 56: Stokes-Leibenzon Model Ω(t) 0 y
Page 57: Free Boundary Problem • ∆p = Q
Page 61 and 62: P. Ya. Polubarinova-Kochina In 1921
Page 63 and 64: P. Ya. Polubarinova-Kochina In 1958
Page 65 and 66: L. A. Galin Lev Alexandrovich Galin
Page 67 and 68: Hele-Shaw problem P. Ya. Polubarino
Page 69 and 70: Papers • P. Ya. Polubarinova-Koch
Page 71 and 72: P. P. Kufarev Pavel Parfenievich Ku
Page 73 and 74: Kufarev’s exact solutions 1947-19
Page 75 and 76: Kufarev’s exact solutions 1947-19
Page 77 and 78: The proof of local existence BIRS,
Page 79 and 80: Flows in Porous Media Random struct
Page 81 and 82: Examples of Porous Media Rock, BIRS
Page 83 and 84: Darcy’s Low Henry Philibert Gaspa
Page 85 and 86: Oil Recovery BIRS, Canada, July 200
Page 87 and 88: Microscopic Image Beginning of reco
Page 89 and 90: Fingering Phenomenon Modelling by t
Page 91 and 92: UK CONTRIBUTION BIRS, Canada, July
Page 93 and 94: Saffman-Taylor Finger Mathematical
Page 95 and 96: Philip G. Saffman Philip Geoffrey S
Page 97 and 98: Conformal formulation Saffman-Taylo
Page 99 and 100: Selection Problem This proposal was
Page 101 and 102: Richardson: Modern Period BIRS, Can
Page 103 and 104: MODERN PERIOD 1981-PRESENT • Nowa
Page 105 and 106: Evolution Geometry Björn Gustafsso
Page 107 and 108: Other Models Witten, Sander, Hastin
Page 109 and 110:
Multi-dimensional flows, PDE Caffar
Page 111 and 112:
Integrable Systems (2000-2007) P.Wi
Page 113 and 114:
Integrable Systems (2000-2007) The
Page 115 and 116:
Recommended Reading Two monographs:
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