Non-classical equations of mixed type and their applications in gas dynamics
type: Item
instance of: scholarly article
title: Non-classical equations of mixed type and their applications in gas dynamics
zbMATH Open document ID: 0862.35077
published in: ISNM. International Series of Numerical Mathematics
publication date: 1993-01-23T00:00:00Z
review text: The book contains the author's results on solvability of boundary value problems for linear equations of mixed type and their applications in transonic gas dynamics. It consists of Introduction, five Chapters and Appendix. In the Introduction a brief historical review and the structure of the book are given. In Chapter 1 the author analyses the behavior of characteristic curves on the plane for the cases which were not included in Cibrario's theory. The analysis uses classical methods of the qualitative theory of ordinary differential equations. In Chapter 2, which is central in the book, nonclassical equations of mixed type with smooth coefficients are treated. The equations are called nonclassical if they are irreducible by the transformation of variables to well-known equations having a single type degeneracy line that is not tangent to the characteristic direction at any point or, on the contrary, is a particular characteristic. The solvability of boundary value problems for wide classes of those equations in Sobolev spaces is studied. In Chapter 3 similar problems for model equations are considered. In Chapters 4 and 5 gasdynamical problems such as a flow in a Laval nozzle, nonisentropic flows and acoustic fields in nonuniform flows are treated. In the Appendix numerical results for acoustic vibrations in a Laval nozzle, disturbances in flows with perforated boundaries and a model jet radiation are presented.
Mathematics Subject Classification ID: 35M10
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 35-02
zbMATH DE Number: 108438
zbMATH Keywords: linear equations of mixed type
zbMATH Keywords: transonic gas dynamics
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: flow in a Laval nozzle
zbMATH Keywords: nonisentropic flows
zbMATH Keywords: acoustic fields in nonuniform flows
zbMATH Keywords: numerical results
author: Alexander Kuz'min
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 108438