Similarity solutions for liquid metal systems near a sharply cornered conductive region

Je Chiang Tsai

doi:10.1016/j.jmaa.2009.01.030

Similarity solutions for liquid metal systems near a sharply cornered conductive region

Je Chiang Tsai^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We study the boundary value problem (P_{m, 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 (P_{m, a}) for the physical interesting case: m < - 1 and a ≥ 0.

Original language	English
Pages (from-to)	364-384
Number of pages	21
Journal	Journal of Mathematical Analysis and Applications
Volume	355
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2009.01.030
Publication status	Published - 2009 Jul 1
Externally published	Yes

Keywords

Boundary value problem
Initial value problem
Phase plane analysis
Similarity solution
Third order differential equation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2009.01.030

Cite this

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title = "Similarity solutions for liquid metal systems near a sharply cornered conductive region",

abstract = "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.",

keywords = "Boundary value problem, Initial value problem, Phase plane analysis, Similarity solution, Third order differential equation",

author = "Tsai, \{Je Chiang\}",

note = "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.",

year = "2009",

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doi = "10.1016/j.jmaa.2009.01.030",

language = "English",

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journal = "Journal of Mathematical Analysis and Applications",

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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

UR - https://www.scopus.com/pages/publications/61349175183

UR - https://www.scopus.com/pages/publications/61349175183#tab=citedBy

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 -

Similarity solutions for liquid metal systems near a sharply cornered conductive region

Abstract

Keywords

ASJC Scopus subject areas

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