Hyperbolic Conservation Laws, Integral Balance Laws and Regularity of Fluxes

doi:10.1007/s42967-023-00298-2

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (4): 2048-2063.doi: 10.1007/s42967-023-00298-2

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Hyperbolic Conservation Laws, Integral Balance Laws and Regularity of Fluxes

Matania Ben-Artzi¹, Jiequan Li^2,3

1 Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904, Israel;
2 Academy for Multidisciplinary Studies, Capital Normal University, Beijing 100048, China;
3 State Key Laboratory for Turbulence Research and Complex System, Peking University, Beijing 100871, China

Received:2023-05-30 Revised:2023-07-08 Accepted:2023-07-09 Published:2024-12-20
Contact: Matania Ben-Artzi,E-mail:mbartzi@math.huji.ac.il;Jiequan Li,E-mail:jiequan@cnu.edu.cn E-mail:mbartzi@math.huji.ac.il;jiequan@cnu.edu.cn

Abstract

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.

Key words: Balance laws, Hyperbolic conservation laws, Finite volume approximations, Flux regularity, Consistency

Matania Ben-Artzi, Jiequan Li. Hyperbolic Conservation Laws, Integral Balance Laws and Regularity of Fluxes[J]. Communications on Applied Mathematics and Computation, 2024, 6(4): 2048-2063.

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Hyperbolic Conservation Laws, Integral Balance Laws and Regularity of Fluxes

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