| Abstract: | We 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. |
