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

E. Weinan, Robert V. Kohn

Research output: Contribution to journalArticle

13 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)981-1000
Number of pages20
JournalCommunications on Pure and Applied Mathematics
Volume44
Issue number8-9
DOIs
StatePublished - Jan 1 1991
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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