Preprint 1998-039

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, mailto:bressan@sissa.it
P. Goatin, mailto:goatin@sissa.it
Publishing information:
Comments:
Submitted by:
mailto:goatin@sissa.it December 10 1998.


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