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

2011/06/28 by Cleopatra Christoforou, Christoforou, Cleopatra, Laura V. Spinolo +1
Engineering · Mathematics · #35K51 #35L50 #35L65 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:35K51 #msc:35L50 #msc:35L65

paper · pdf · doi:10.48550/arxiv.1106.5603

20 pages

arxiv created 2011/06/28 · openalex publication_date 2011/06/28 · arxiv updated 2011/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 non conservative 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 genuinely nonlinearity nor linear degeneracy of the characteristic fields.

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