Hyperbolic Conservation Laws, Integral Balance Laws and Regularity of Fluxes

Matania Ben-Artzi*, Jiequan Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Hyperbolic conservation laws arise in the context of continuum physics, and are mathematically presented in differential form and understood in the distributional (weak) sense. The formal application of the Gauss-Green theorem results in integral balance laws, in which the concept of flux plays a central role. This paper addresses the spacetime viewpoint of the flux regularity, providing a rigorous treatment of integral balance laws. The established Lipschitz regularity of fluxes (over time intervals) leads to a consistent flux approximation. Thus, fully discrete finite volume schemes of high order may be consistently justified with reference to the spacetime integral balance laws.

Original languageEnglish
Pages (from-to)2048-2063
Number of pages16
JournalCommunications on Applied Mathematics and Computation
Volume6
Issue number4
DOIs
StatePublished - Dec 2024

Bibliographical note

Publisher Copyright:
© Shanghai University 2023.

Keywords

  • Balance laws
  • Consistency
  • Finite volume approximations
  • Flux regularity
  • Hyperbolic conservation laws
  • Primary 35L65
  • Secondary 76M12 · 65M08

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