Preprint 2000003
LongTime 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 subcharacteristic condition
we show that, as the time tends to infinity, nonnegative
component u of solutions tends towards a diffusion wave of
the convectiondiffusion equation given by the standard
ChapmanEnskog expansion, in the $L^p$ norm, at a rate
faster than $t^{ (p1)/2p}$. This diffusion wave carries
an invariant mass and has a selfsimilar structure.
 Paper:
 Available as PostScript.
 Author(s):
 H. Liu,
<hailiang.liu@mathematik.unimagdeburg.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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Last modified: Thu Jan 13 16:37:50 2000