Stability of L$^\infty$ Solutions of Temple Class Systems
A. Bressan and P. Goatin
Let $u_t+f(u)_x=0$ be a strictly hyperbolic,
genuinely nonlinear system of conservation laws of Temple class.
In this paper, a continuous
semigroup of solutions is constructed on a domain of
$\L^\infty$ functions, with possibly unbounded variation.
Trajectories depend Lipschitz
continuously on the initial data, in the $\L^1$ distance.
Moreover, we show that a weak solution of the Cauchy problem coincides with
the corresponding semigroup trajectory if and only if it satisfies
an entropy condition of Oleinik type, concerning
the decay of positive waves.
- Available as PostScript.
- Stability of L$^\infty$ solutions of Temple class systems
- A. Bressan,
- P. Goatin,
- Publishing information:
- Submitted by:
December 10 1998.
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 <email@example.com>
Last modified: Thu Dec 10 11:26:21 1998