Classification of CodimensionOne Riemann Solutions
 Stephen Schecter,
 Bradley J. Plohr,
 Dan Marchesin
 … show all 3 hide
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We investigate solutions of Riemann problems for systems of two conservation laws in one spatial dimension. Our approach is to organize Riemann solutions into strata of successively higher codimension. The codimensionzero stratum consists of Riemann solutions that are structurally stable: the number and types of waves in a solution are preserved under small perturbations of the flux function and initial data. Codimensionone Riemann solutions, which constitute most of the boundary of the codimensionzero stratum, violate structural stability in a minimal way. At the codimensionone stratum, either the qualitative structure of Riemann solutions changes or solutions fail to be parameterized smoothly by the flux function and the initial data. In this paper, we give an overview of the phenomena associated with codimensionone Riemann solutions. We list the different kinds of codimensionone solutions, and we classify them according to their geometric properties, their roles in solving Riemann problems, and their relationships to wave curves.
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 Title
 Classification of CodimensionOne Riemann Solutions
 Journal

Journal of Dynamics and Differential Equations
Volume 13, Issue 3 , pp 523588
 Cover Date
 20010701
 DOI
 10.1023/A:1016634307145
 Print ISSN
 10407294
 Online ISSN
 15729222
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 conservation law
 Riemann problem
 viscous profile
 Authors

 Stephen Schecter ^{(1)}
 Bradley J. Plohr ^{(2)}
 Dan Marchesin ^{(2)}
 Author Affiliations

 1. Mathematics Department, North Carolina State University, Raleigh, North Carolina, 27695
 2. Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460, Rio de Janeiro, RJ, Brazil