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Sup-norm stability for Glimm’s scheme. (English) Zbl 0792.35120
We consider the Cauchy problem for a general $$N \times N$$ system of conservation laws. Existence of solutions was proved by Glimm using his celebrated random choice scheme. In this paper, we obtain a third order interaction estimate analogous to that obtained by Glimm for $$2\times 2$$ systems. By using this estimate, and identifying a global cancellation effect, we obtain $$L^ \infty$$-stability for solutions generated by Glimm’s scheme. As an immediate consequence we have $$L^ 1$$-stability and $$L^ \infty$$-decay, obtained by Temple for $$2\times 2$$ systems.
Reviewer: R.Young (New York)

##### MSC:
 35L65 Hyperbolic conservation laws 35L45 Initial value problems for first-order hyperbolic systems 35L67 Shocks and singularities for hyperbolic equations 35D05 Existence of generalized solutions of PDE (MSC2000)
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##### References:
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