Preprint 1999-038

Viscous Profiles for Traveling Waves of Scalar Balance Laws: The Canard Case

J. Härterich

Abstract: We study the question whether some traveling waves of a scalar balance law $u_t + f(u)_x =g(u)$ can be approximated by traveling waves of the viscous regularization $u_t + f(u)_x= \varepsilon u_{xx}+g(u)$ such that the wave speed of the viscous traveling waves tends to the wave speed of the hyperbolic traveling wave as $\varepsilon$ tends to zero. Also we require the profiles to converge in $L^1$. Using a blow-up method from geometrical singular perturbation theory we give a positive result for the monotone traveling waves which occur at isolated wave speeds.

Available as PostScript.
J. Härterich, <>
Publishing information:
Submitted by:
<> November 29 1999.

[ 1996 | 1997 | 1998 | 1999 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <>
Last modified: Tue Nov 30 14:06:18 1999