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

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2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)364-384
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume355
Issue number1
DOIs
Publication statusPublished - 2009 Jul 1

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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