TY - JOUR
T1 - Similarity solutions for liquid metal systems near a sharply cornered conductive region
AU - Tsai, Je Chiang
N1 - Funding Information:
This paper is dedicated to the memory of Erh-Mao Tsai (2007–2008), my child. This work was partially supported by the National Science Council of the Republic of China under the contract NSC 96-2115-M-194-003-MY3. The author would like to thank Professor Bernard Brighi for his valuable suggestions, and the referees for helpful comments on this paper.
PY - 2009/7/1
Y1 - 2009/7/1
N2 - We study the boundary value problem (Pm, a): f‴ + [(m + 1) / 2] f f″ - m f′ 2 = 0 on (0, + ∞), subject to the boundary conditions f (0) = a ∈ R, f′ (0) = - 1 and f′ (+ ∞) = 0. The problem arises in the study of similarity solutions for high frequency excitation of liquid metal systems in an antisymmetric magnetic field. We give a complete picture of solutions of (Pm, a) for the physical interesting case: m < - 1 and a ≥ 0.
AB - We study the boundary value problem (Pm, a): f‴ + [(m + 1) / 2] f f″ - m f′ 2 = 0 on (0, + ∞), subject to the boundary conditions f (0) = a ∈ R, f′ (0) = - 1 and f′ (+ ∞) = 0. The problem arises in the study of similarity solutions for high frequency excitation of liquid metal systems in an antisymmetric magnetic field. We give a complete picture of solutions of (Pm, a) for the physical interesting case: m < - 1 and a ≥ 0.
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 - 10.1016/j.jmaa.2009.01.030
DO - 10.1016/j.jmaa.2009.01.030
M3 - Article
AN - SCOPUS:61349175183
SN - 0022-247X
VL - 355
SP - 364
EP - 384
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -