Similarity solutions for a model arising from high frequency excitation of liquid metal in an antisymmetric magnetic field

Bernard Brighi, Je Chiang Tsai

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Abstract

The study of similarity solutions is necessary for the understanding of the dynamical behaviour of the fluid in the high-frequency excitation of liquid metal embedded in an antisymmetric magnetic field. Such similarity solutions are governed by the third-order non-linear equation: f‴+m+1/2 ff″2 = 0 on (0, + ∞), subject to the boundary conditions f(0) = a ∈ ℝ, f′(0) = -1 and f′(+∞) = 0. The remaining unsolved case is for m ε (- 1, 0). In this paper, we will give an almost complete solution structure of this problem for m ε (- 1, 0), which complements earlier results in literature.

Original languageEnglish
Pages (from-to)157-195
Number of pages39
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume77
Issue number2
DOIs
Publication statusPublished - 2012 Apr 1

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Keywords

  • boundary-value problem
  • initial-value problem
  • phase plane analysis
  • similarity solution
  • third-order differential equation

ASJC Scopus subject areas

  • Applied Mathematics

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