Simple waves do not avoid eigenvalue crossings

2009/06/08 by Lyuba Chumakova, Esteban G. Tabak · 1 citation
Mathematics · Engineering · #Navier-Stokes equation solutions #Fluid Dynamics and Turbulent Flows #Advanced Mathematical Physics Problems

paper · doi:10.1002/cpa.20288

Abstract

Abstract General one‐parameter families of matrices avoid eigenvalue crossings. It is shown that the matrices associated with the simple waves of nonlinear systems of conservation laws do not obey this rule: a subset of simple waves with nonzero measure has crossing eigenvalues. © 2009 Wiley Periodicals, Inc.

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• Nonlinear stability of two-layer shallow water flows with a free surface. [europepmc]

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