Similarity solutions for liquid metal systems near a sharply cornered conductive region
type: Item
instance of: scholarly article
title: Similarity solutions for liquid metal systems near a sharply cornered conductive region
zbMATH Open document ID: 1177.34044
author: Je-Chiang Tsai
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-05-19T00:00:00Z
review text: The following boundary value problem \[ \begin{cases} f''' + [(m+1)/2]ff'' - m {f'}^2 = 0 \quad \text{on}\;(0,+\infty), \\ f(0)=a \in {\mathbb R}, \quad f'(0)=-1, \quad f'(+\infty) = 0 \end{cases} \] is considered. The problem arises in the study of similarity solutions for high frequency excitation of liquid metal systems in an antisymmetric magnetic field. A complete picture of solutions is given for the physical interesting case when \(m<-1\) and \(a\geq 0\).
reviewed by: Satoshi Tanaka
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 76W05
zbMATH DE Number: 5555257
zbMATH Keywords: similarity solution
zbMATH Keywords: third order differential equation
zbMATH Keywords: boundary value problem
zbMATH Keywords: initial value problem
zbMATH Keywords: phase plane analysis
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.01.030
OpenAlex ID: W2055048845
cites work: Eigensolutions in Boundary-Layer Flow Adjacent to a Stretching Wall
cites work: On a family of differential equations for boundary layer approximations in porous media
cites work: On a similarity boundary layer equation
cites work: Asymptotic behavior of the unbounded solutions of some boundary layer equations
cites work: Blowing-up coordinates for a similarity boundary layer equation
cites work: Q3419866
cites work: Q4859268
cites work: On a differential equation of boundary-layer theory
cites work: Q5285417
cites work: Nonuniqueness of solutions to differential equations for boundary-layer approximations in porous media
cites work: Similarity solutions of differential equations for boundary layer approximations in porous media
cites work: Q5330830
cites work: Diffusion of an alternating magnetic field into a sharply cornered conductive region
cites work: More Accurate Skin-Depth Approximations
cites work: Q4174990
cites work: Reflections on magnetohydrodynamics
cites work: The structure of solutions for a third order differential equation in boundary layer theory
cites work: Q4319550
cites work: On the differential equations of the simplest boundary-layer problems
DOI: 10.1016/J.JMAA.2009.01.030
description: scientific article; zbMATH DE number 5555257