Singularities of multivalued solutions of nonlinear differential equations, and nonlinear phenomena
type: Item
instance of: scholarly article
title: Singularities of multivalued solutions of nonlinear differential equations, and nonlinear phenomena
zbMATH Open document ID: 0562.35008
DOI: 10.1007/BF00580702
published in: Acta Applicandae Mathematicae
publication date: 1985-01-01T00:00:00Z
review text: It is shown how the geometrical theory of nonlinear partial differential equations and the theory of singularities of maps can be used to obtain a general scheme for constructing shock waves from smooth multivalued solutions. This scheme is illustrated by examples from gas dynamics, mechanics, acoustics and thermodynamics. The paper is popularly written and includes an introductive exposition of multivalued solutions, symmetries and conservation laws of differential equations on manifolds.
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35G20
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
Mathematics Subject Classification ID: 58J47
Mathematics Subject Classification ID: 58K35
zbMATH DE Number: 3895483
zbMATH Keywords: geometrical theory
zbMATH Keywords: singularities of maps
zbMATH Keywords: shock waves
zbMATH Keywords: smooth multivalued solutions
zbMATH Keywords: gas dynamics
zbMATH Keywords: mechanics
zbMATH Keywords: acoustics
zbMATH Keywords: thermodynamics
zbMATH Keywords: symmetries
zbMATH Keywords: conservation laws
author: Valentin Lychagin
reviewed by: S. V. Duzhin
MaRDI profile type: Publication
cites work: Q4160117
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description: scientific article