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

收稿日期:2023-05-30 修回日期:2023-07-08 接受日期:2023-07-09 发布日期:2024-12-20
通讯作者: 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
基金资助:
The second author (the late Professor Jiequan Li) was supported by the NSFC (Nos.11771054,12072042,91852207),the Sino-German Research Group Project (No.GZ1465),and the National Key Project GJXM92579.

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

摘要/Abstract

摘要： 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.

关键词: Balance laws, Hyperbolic conservation laws, Finite volume approximations, Flux regularity, Consistency

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

Hyperbolic Conservation Laws, Integral Balance Laws and Regularity of Fluxes

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