TY - JOUR

T1 - Similarity solutions for a model arising from high frequency excitation of liquid metal in an antisymmetric magnetic field

AU - Brighi, Bernard

AU - Tsai, Je Chiang

N1 - Funding Information:
Université de Haute Alsace and National Science Council of Taiwan under the contract NSC 96-2115-M-194-003-MY3.

PY - 2012/4

Y1 - 2012/4

N2 - 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.

AB - 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.

KW - boundary-value problem

KW - initial-value problem

KW - phase plane analysis

KW - similarity solution

KW - third-order differential equation

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U2 - 10.1093/imamat/hxr012

DO - 10.1093/imamat/hxr012

M3 - Article

AN - SCOPUS:84859018283

SN - 0272-4960

VL - 77

SP - 157

EP - 195

JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

IS - 2

ER -