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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Last modified: Thu Jan 13 16:37:50 2000