Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Boundary layers for self-similar viscous approximations of nonlinear hyperbolic systems

Authors: Cleopatra Christoforou and Laura V. Spinolo
Journal: Quart. Appl. Math. 71 (2013), 433-453
MSC (2010): Primary 35L65, 35L50, 35K51
DOI: https://doi.org/10.1090/S0033-569X-2013-01284-6
Published electronically: May 16, 2013
MathSciNet review: 3112822
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Abstract: We provide a precise description of the set of residual boundary conditions generated by the self-similar viscous approximation introduced by Dafermos et al. We then apply our results, valid for both conservative and nonconservative systems, to the analysis of the boundary Riemann problem and we show that, under appropriate assumptions, the limits of the self-similar and the classical vanishing viscosity approximation coincide. We require neither genuine nonlinearity nor linear degeneracy of the characteristic fields.

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Additional Information

Cleopatra Christoforou
Affiliation: Department of Mathematics and Statistics, University of Cyprus, 1678 Nicosia, Cyprus
Email: Christoforou.Cleopatra@ucy.ac.cy

Laura V. Spinolo
Affiliation: IMATI-CNR, via Ferrata 1, 27100 Pavia, Italy
Email: spinolo@imati.cnr.it

DOI: https://doi.org/10.1090/S0033-569X-2013-01284-6
Keywords: Hyperbolic systems, boundary Riemann problem, self-similar viscous approximation, vanishing viscosity, boundary layer.
Received by editor(s): June 15, 2011
Published electronically: May 16, 2013
Dedicated: Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday
Article copyright: © Copyright 2013 Brown University