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

E. Weinan; Robert V. Kohn

doi:10.1002/cpa.3160440811

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

E. Weinan
, Robert V. Kohn

Mathematics

Research output: Contribution to journal › Article › peer-review

15 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 language	English (US)
Pages (from-to)	981-1000
Number of pages	20
Journal	Communications on Pure and Applied Mathematics
Volume	44
Issue number	8-9
DOIs	https://doi.org/10.1002/cpa.3160440811
State	Published - 1991

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1002/cpa.3160440811

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

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.",

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AU - Weinan, E.

AU - Kohn, Robert V.

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N2 - 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.

AB - 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.

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UR - https://www.scopus.com/pages/publications/84990627098#tab=citedBy

U2 - 10.1002/cpa.3160440811

DO - 10.1002/cpa.3160440811

M3 - Article

AN - SCOPUS:84990627098

SN - 0010-3640

VL - 44

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EP - 1000

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 8-9

ER -

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

Abstract

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