Preprint 1998039
Stability of L$^\infty$ Solutions of Temple Class Systems
A. Bressan and P. Goatin
Abstract:
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.
 Paper:
 Available as PostScript.
 Title:
 Stability of L$^\infty$ solutions of Temple class systems
 Author(s):
 A. Bressan,
<bressan@sissa.it>
 P. Goatin,
<goatin@sissa.it>
 Publishing information:

 Comments:

 Submitted by:

<goatin@sissa.it>
December 10 1998.
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