### 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.

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Title:
Stability of L$^\infty$ solutions of Temple class systems
Author(s):
A. Bressan, <bressan@sissa.it>
P. Goatin, <goatin@sissa.it>
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