Preprint 2000-003

Long-Time Diffusive Behavior of Solutions to a Hyperbolic Relaxation System

H. Liu and R. Natalini

Abstract: We study the large time behavior of the solutions to the Cauchy problem for a simple semilinear system with relaxation source. Under the sub-characteristic condition we show that, as the time tends to infinity, nonnegative component u of solutions tends towards a diffusion wave of the convection-diffusion equation given by the standard Chapman-Enskog expansion, in the $L^p$ norm, at a rate faster than $t^{ -(p-1)/2p}$. This diffusion wave carries an invariant mass and has a self-similar structure.

Available as PostScript.
H. Liu, <>
R. Natalini, <>
Publishing information:
Quaderno IAC n. 17/1999
Submitted by:
<> January 13 2000.

[ 1996 | 1997 | 1998 | 1999 | 2000 | 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: Thu Jan 13 16:37:50 2000