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.


Paper:
Available as PostScript.
Author(s):
H. Liu, <hailiang.liu@mathematik.uni-magdeburg.de>
R. Natalini, <natalini@iac.rm.cnr.it>
Publishing information:
Quaderno IAC n. 17/1999
Comments:
Submitted by:
<natalini@iac.rm.cnr.it> January 13 2000.


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