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

E. Weinan, Robert Kohn

Research output: Contribution to journalArticle

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 - 1991

Fingerprint

Initial Value Problem
Linearly
Particle Method
Formulation
Computational Grid
Existence and Uniqueness
Exact Solution
Regularity

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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