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.
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Last modified: Thu Dec 10 11:26:21 1998