The initial-value problem for measure-valued solutions of a canonical 2 × 2 system with linearly degenerate fields

✍ Scribed by E. Weinan; Robert V. Kohn

• Publisher: John Wiley and Sons
• Year: 1991
• Tongue: English
• Weight: 778 KB
• Volume: 44
• Category: Article
• ISSN: 0010-3640
• DOI: 10.1002/cpa.3160440811

✦ Synopsis

Abstract

We discuss Serre's restricted formulation of the notion of a measure‐valued solution, for a 2 × 2 system whose characteristic fields are both linearly degenerate. We prove existence, uniqueness, and regularity results for this formulation. As an application, we prove the convergence of a particle method when the high‐frequency component of the exact solution is not resolved by the computational grid.