A connection between viscous profiles and singular ODEs
Abstract
We deal with the viscous profiles for a class of mixed hyperbolicparabolic systems. We focus, in particular, on the case of the compressible Navier Stokes equation in one space variable written in Eulerian coordinates. We describe the link between these profiles and a singular ordinary differential equation in the form $$ dV / dt = F(V) / z (V) . $$ Here $V \in R^d$ and the function F takes values into $R^d$ and is smooth. The real valued function z is as well regular: the equation is singular in the sense that z (V) can attain the value 0.
 Publication:

arXiv eprints
 Pub Date:
 January 2008
 arXiv:
 arXiv:0801.4532
 Bibcode:
 2008arXiv0801.4532B
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Classical Analysis and ODEs;
 35M10;
 35L65;
 34A99
 EPrint:
 6 pages, minor changes