An analytical treatment of the formation of one-dimensional steady shock waves in uniform and diverging ducts
type: Item
instance of: scholarly article
title: An analytical treatment of the formation of one-dimensional steady shock waves in uniform and diverging ducts
zbMATH Open document ID: 0543.76090
DOI: 10.1016/0377-0427(84)90057-8
author: F. A. Howes
published in: Journal of Computational and Applied Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Boundary value problems of the form \((*)\quad \epsilon(d^ 2y/dx^ 2)=f(x,y)(dy/dx)+g(x,y), a<x<b\), y(a,\(\epsilon)\), y(b,\(\epsilon)\) prescribed, whose solutions model the behavior of one-dimensional steady shock waves in ducts of uniform and variable cross-section have been studied by singular perturbation techniques. The sufficient conditions for the existence of solutions which have a 'shock layer structure' at a point \(x_ 0\in(a,b)\) have been found, the position \(x_ 0\) of the shock layer has been located, and the 'states' separated by a solution of (*) having such an interior transition are determined.
Mathematics Subject Classification ID: 76L05
Mathematics Subject Classification ID: 76M45
Mathematics Subject Classification ID: 76D10
zbMATH DE Number: 3864826
zbMATH Keywords: uniform and diverging ducts
zbMATH Keywords: Rankine-Hugoniot condition, Prandtl's relation
zbMATH Keywords: Boundary value problems
zbMATH Keywords: one-dimensional steady shock waves
zbMATH Keywords: ducts of uniform and variable cross-section
zbMATH Keywords: sufficient conditions for the existence
zbMATH Keywords: shock layer structure
zbMATH Keywords: interior transition
MaRDI profile type: Publication
full work available at URL: 0377-0427(84)90057-8
OpenAlex ID: W2028299084
cites work: A Boundary Value Problem for a Nonlinear Differential Equation with a Small Parameter
cites work: Q5801144
cites work: Boundary-interior layer interactions in nonlinear singular perturbation theory
cites work: On Non‐Linear Ordinary Differential Equations of Boundary Layer Type
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description: scientific article; zbMATH DE number 3864826