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Preprint 2009-041

A connection between viscous profiles and singular ODEs

Stefano Bianchini and Laura V. Spinolo

Abstract: We deal with the viscous profiles for a class of mixed hyperbolic–parabolic 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)/ζ(V).

Here V is in Rd and the function F takes values into Rd and is smooth. The real valued function ζ is as well regular: the equation is singular in the sense that ζ(V) can attain the value 0.

Paper:
Available as PDF (105 Kbytes).
Author(s):
Stefano Bianchini
Laura V. Spinolo
Publishing information:
Comments:
Submitted by:
; 2009-07-10.