Free boundary problems for the unsteady transonic small disturbance equation: Transonic regular reflection
type: Item
instance of: scholarly article
title: Free boundary problems for the unsteady transonic small disturbance equation: Transonic regular reflection
zbMATH Open document ID: 1015.76038
author: Sunčica Čanić
author: Barbara Lee Keyfitz
author: Eun Heui Kim
published in: Methods and Applications of Analysis
publication date: 2002-06-19T00:00:00Z
review text: Using a free boundary problem approach, the authors formulate and solve a transonic regular reflection problem for unsteady transonic small disturbance equation. The method applies to self-similar shock reflection when the incident shock angle is large enough to permit a regular reflection configuration with a subsonic state behind the reflected shock. The main result is the existence theorem for nonuniform subsonic flow behind the reflected schok. The flow velocity satisfies a quasilinear elliptic equation which is coupled to Rankine-Hugoniot equations for reflected shock, forming a free boundary problem on a part of the boundary. Because the equation is not uniformly elliptic in the entire domain, a cut off is introduced to give a bounded domain, together with cut offs for the coefficients.
Mathematics Subject Classification ID: 76H05
Mathematics Subject Classification ID: 76L05
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 1757304
zbMATH Keywords: free boundary problem
zbMATH Keywords: transonic regular reflection
zbMATH Keywords: unsteady transonic small disturbance equation
zbMATH Keywords: self-similar shock reflection
zbMATH Keywords: existence
zbMATH Keywords: quasilinear elliptic equation
zbMATH Keywords: Rankine-Hugoniot equations
reviewed by: Silvio Nocilla
MaRDI profile type: Publication
full work available at URL: maa.2000.v7.n2.a4
OpenAlex ID: W1520178774
DOI: 10.4310/MAA.2000.V7.N2.A4
description: scientific article; zbMATH DE number 1757304