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Original Articles

Approximate Waiting-Time for a Thin Liquid Drop Spreading under Gravity

Pages 102-109 | Received 01 Feb 2002, Published online: 21 Jan 2013

References

  • Baikov , V A , Gazizov , R K and Ibragimov , N H . 1988 . Approximate Symmetries . Math. Sbornik , 136 : 435 – 450 . [English translation in Math. USSR Sbornik 64 Nr. 2 (1989), 427–441]
  • Baikov , V A , Gazizov , R K and Ibragimov , N H . 1989 . Perturbation Methods in Group Analysis, in Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki . Noveishie Dostizheniya , 34 : 85 – 147 . [English translation in J. Soviet Math. 55 (1991), 1450–1490]
  • Baikov , V A and Ibragimov , N H . 2000 . Continuation of Approximate Transformation Groups via Multiple Scales Method . Nonlinear Dynamics , 22 : 3 – 13 .
  • Bluman , G W and Kumei , S . 1989 . Symmetries and Differential Equations , New York : Springer .
  • Dussan , E V and Davis , S H . 1974 . On the Motion of a Fluid-Fluid Interface Along a Solid Surface . J. Fluid Mech. , 65 : 71 – 95 .
  • Dussan , E V . 1979 . On the Spreading of Liquids on Solid Surfaces: Static and Dynamic Contact Lines . Ann. Rev. Fluid Mech. , 11 : 371 – 400 .
  • Euler , M , Euler , N and Köhler , A . 1994 . On the Construction of Approximate Solutions for a Multidimensional Nonlinear Heat Equation . J. Phys. A: Math. Gen. , 27 : 2083 – 2092 .
  • Euler , N , Shul’ga , M W and Steeb , W H . 1992 . Approximate Symmetries and Approximate Solutions for a Multidimensional Landau–Ginzburg Equation . J. Phys. A: Math. Gen. , 25 : L1095 – L1103 .
  • Euler , N and Euler , M . 1994 . Symmetry Properties of the Approximations of Multidimensional Generalized van der Pol Equations . J. Nonlin. Math. Phys. , 1 : 41 – 59 .
  • Fushchich , W I and Shtelen , W M . 1989 . On Approximate Symmetry and Approximate Solutions of the Nonlinear Wave Equation with a Small Parameter . J. Phys. A: Math. Gen. , 22 : L887 – L890 .
  • Hocking , L M . 1992 . Rival Contact-Angle Models and the Spreading of Drops . J. Fluid Mech. , 239 : 671 – 681 .
  • Kath , W L and Cohen , D S . 1982 . Waiting-Time Behaviour in a Nonlinear Diffusion Equation . Studies in Applied Mathematics , 67 : 79 – 105 .
  • Mahomed , F M and Qu , C . 2000 . Approximate Conditional Symmetries for Partial Differential Equations . J. Phys. A: Math. Gen. , 33 : 343 – 356 .
  • Momoniat , E , Mason , D P and Mahomed , F M . 2001 . Non-Linear Diffusion of an Axisymmetric Thin Liquid Drop: Group Invariant Solution and Conservation Law . Int. J. Non-Linear Mech. , 36 : 879 – 885 .
  • Nayfeh , A . 1973 . Perturbation Methods , New York : John Wiley & Sons .
  • Ovsiannikov , L V . 1982 . Group Analysis of Differential Equations , New York : Academic Press .

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