Sup‐norm stability for Glimm's scheme | Zendy

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Sup‐norm stability for Glimm's scheme

Author(s) -

Young Robin

Publication year - 1993

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.3160460605

Subject(s) - mathematics , norm (philosophy) , conservation law , stability (learning theory) , scheme (mathematics) , cauchy problem , cauchy distribution , initial value problem , mathematical analysis , law , computer science , machine learning , political science

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 L 1 ‐stability and L ∞ ‐decay, obtained by Temple for 2×2 systems. © 1993 John Wiley & Sons, Inc.

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