Representation of weak limits and definition of nonconservative products

Philippe G. LeFloch; Athanasios E. Tzavaras

doi:10.1137/S0036141098341794

Representation of weak limits and definition of nonconservative products

Philippe G. LeFloch^*, Athanasios E. Tzavaras

^*Corresponding author for this work

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

87 Scopus citations

Abstract

The goal of this article is to show that the notion of generalized graphs is able to represent the limit points of the sequence {g(u_n) du_n} in the weak-(black star sing) topology of measures when {u_n} is a sequence of continuous functions of uniformly bounded variation. The representation theorem induces a natural definition for the nonconservative product g(u) du in a BV context. Several existing definitions of nonconservative products are then compared, and the theory is applied to provide a notion of solutions and an existence theory to the Riemann problem for quasi-linear, strictly hyperbolic systems.

Original language	English (US)
Pages (from-to)	1309-1342
Number of pages	34
Journal	SIAM Journal on Mathematical Analysis
Volume	30
Issue number	6
DOIs	https://doi.org/10.1137/S0036141098341794
State	Published - Oct 1999
Externally published	Yes

Keywords

Hyperbolic systems
Nonconservative products
Self-similar solution
Shock wave

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/S0036141098341794

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AU - Tzavaras, Athanasios E.

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AB - The goal of this article is to show that the notion of generalized graphs is able to represent the limit points of the sequence {g(un) dun} in the weak-(black star sing) topology of measures when {un} is a sequence of continuous functions of uniformly bounded variation. The representation theorem induces a natural definition for the nonconservative product g(u) du in a BV context. Several existing definitions of nonconservative products are then compared, and the theory is applied to provide a notion of solutions and an existence theory to the Riemann problem for quasi-linear, strictly hyperbolic systems.

KW - Hyperbolic systems

KW - Nonconservative products

KW - Self-similar solution

KW - Shock wave

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ER -

Representation of weak limits and definition of nonconservative products

Abstract

Keywords

ASJC Scopus subject areas

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