TY - JOUR
T1 - The initial‐value problem for measure‐valued solutions of a canonical 2 × 2 system with linearly degenerate fields
AU - Weinan, E.
AU - Kohn, Robert V.
PY - 1991
Y1 - 1991
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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U2 - 10.1002/cpa.3160440811
DO - 10.1002/cpa.3160440811
M3 - Article
AN - SCOPUS:84990627098
SN - 0010-3640
VL - 44
SP - 981
EP - 1000
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 8-9
ER -