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Original Articles

Lubrication approximation with prescribed nonzero contact anggle

Pages 2077-2164 | Published online: 02 Nov 2010

References

  • Almgren , R. 1996 . Singularity formation in Hele-Shaw bubbles . Phys. Fluids , 4 ( 2 ) : 344 – 352 .
  • Alt , H. -W. and Caffarelli , L. A. 1981 . Existence and regularity for a minimum problem with free boundary . J. Reine Angewandte Math. , U , 325 : 105 – 144 .
  • Bensimon , D. , Kadanoff , L. P. , Liang , S. , Shariman , B. I. and Tang , C. 1996 . Viscous flow in two dimensions . Rev. Mod. Phys. , 3 : 977
  • Beretta , E. , Bertsch , M. and Dal Passo , R. 1995 . Nonnegative solutions of a fourth order nonlinear degenerate parabolic equation . Arch. Rational Mech. Anal. , 129 : 175 – 200 .
  • F. Remis. Viscous flow, fourth order nonlinrat. degenerate equations and singular elliptic problems, in: Free boundary pt.oblvms: theory and applications (J. I. Diaq M. A. Herrero, A. Linan. .J. L. vazques eds.), Pitman Research Notes in Mathematics 323, Longman. Harlow (1995). 40 56.
  • F. Bernis. Integral inequalities with applications to nonlinear degenerate parabolic equations, in: Nonlinear boundary value problems (T. S. Angell, L. P. Cook, R. E. Kleinman, W. E. Olmstead. eds.), Volume in Honor of I. Stakgold, SIAM, Philadelphia (1996), 1 - 9.
  • Rernis , F. and Friedman , A. 1990 . Higher order nonlinem degenrrate parabolic equations. . I. Dzff. Equations, , 83 : 179 – 206 .
  • Bertozzi , A. L. and Pugh , M. 1996 . The lubrication approximation for thin viscous films: regularity and long time behaviour of weak solutions . Comrn. Pure Appl. Math,. , 49 ( 2 ) : 85 – 123 .
  • Brenier , Y. 1991 . Polar factorizat,ion and monotonr rearrangement of vector-valued functions . Comm. Pure Appl. Math. , 44 : 375 – 417 .
  • L. .A. Caffarelli, Allocation maps with general cost functions, in Partial diflerential equations and applications, P. Marcellini, G. G. Talent'i, and E. Tesintini, eds., Lecture Notes in Pure and Applied Mathematics, 177, hrarcel Dekker, Inc., Kew York, (1996), 29-35.
  • Constantin , P. , Dupont , T. F. , Goldstein , R. E. , Kadanoff , L. P. , Shelley , S. -M and Zhou , S. -M. 1993 . Droplet breakup in a model of the Hele-Shaw cell . Phys. Rev. E , 47 ( 6 ) : 4169 – 4181 .
  • Constantin , P. , Goldstein , R. E. , Kadanoff , L. P. and Ri Zhou , S. 1993 . Finite--time singularity formation in Hele-Shaw systems . Phys. Rev. E: , 47 ( 6 ) : 4182 – 4196 .
  • Dussan , E. B. , Rame , E. and Garoff , S. 1991 . On identifying the appropriate bound-ary conditions at a moving contact line: an experimental investigation . J. Fluid Mech. , 230 : 97 – 116 .
  • Elliot , C. M. and Garcke , H. 1996 . On the Cahn-Hillard equation with degenerate mobility . SIAM J. Math. Anal. , 27 ( 2 ) : 401 – 423 .
  • L. Evans, Weak convergence methods for nonlinear partial differential equations. Conference Board of the Mathematical Sciences. Vol. 74 (1990).
  • Gangbo , W. 1994 . An elementary proof of the polar factorization of vector valued functions . Arch. Rational Mech. Anal. , 128 : 381 – 399 .
  • Gangbo , W. and McCann , R. J . 1997 . The geometry of optimal transportatioin . Acta Math. , 177 : 113 – 161 .
  • Goldstein , R. E. , Pesci , A. I. and Shelley , M. J. 1993 . Topological transitions and singularities in viscous flows . Phys. Rev. Lett. , 70 ( 20 ) : 3043 – 3046 .
  • Givens , C. R. and Shortt , R. M. 1984 . A class of Wasserstein metrics for probability distributions. . Michigan Math. J. , 31 : 231 – 240 .
  • Grün , G. 1995 . Degenerate parabolic differential equations of fourth order and a plasticity model with nonlocal hardening . Z. Anal. Anwendungen , 14 : 541 – 574 .
  • Kinderlehrer , D. , Jordan , R. and Otto , F. 1998 . The variational formulation of the Fokker-Planck equation . SIAM J. Math. Anal. , 29 : 1 – 17 .
  • Luckhaus , S. 1990 . Solutions to the two-phase Stefan problem with Gibbs-Thomson law for the melting temperature . EJAM , 1 : 101 – 111 .
  • Otto , F. 1998 . Dynamics of labyrinthine pattern formation in magnetic fluids: a mean-field theory . Arch. Rational Mech. Anal. , 141 : 63 – 103 .
  • Rachev , S. T. 1991 . Probability metrics and the stability of stochastic models , New York : Wiley .

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