Abstract
AbstractWe consider the Cauchy problem for a general N × 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 analagous to that obtained by Glimm for 2×2 systems. By using this estimate, and identifying a global cancellation effect, we obtain L∞‐stability for solutions generated by Glimm's scheme. As an immediate consequence we have L1‐stability and L∞‐decay, obtained by Temple for 2×2 systems. © 1993 John Wiley & Sons, Inc.
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