Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws

doi:10.1007/s42967-022-00224-y

Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (3): 1289-1298.doi: 10.1007/s42967-022-00224-y

• ORIGINAL PAPER • 上一篇

Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws

Matania Ben-Artzi¹, Jiequan Li^2,3

1. Institute of Mathematics, Hebrew University of Jerusalem, 91904, Jerusalem, Israel;
2. Academy of 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:2022-08-18 修回日期:2022-08-18 出版日期:2023-09-20 发布日期:2023-08-29
通讯作者: Jiequan Li,E-mail:jiequan@cnu.edu.cn E-mail:mbartzi@math.huji.ac.il;jiequan@cnu.edu.cn
基金资助:
The first author thanks the Institute of Applied Physics and Computational Mathematics, Beijing, for the hospitality and support. The second author is supported by the NSFC (Nos. 11771054, 12072042,91852207), the Sino-German Research Group Project (No. GZ1465), and the National Key Project GJXM92579. It is a pleasure to thank C. Dafermos and M. Slemrod for many useful comments.

Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws

Matania Ben-Artzi¹, Jiequan Li^2,3

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

Received:2022-08-18 Revised:2022-08-18 Online:2023-09-20 Published:2023-08-29
Contact: Jiequan Li,E-mail:jiequan@cnu.edu.cn E-mail:mbartzi@math.huji.ac.il;jiequan@cnu.edu.cn
Supported by:
The first author thanks the Institute of Applied Physics and Computational Mathematics, Beijing, for the hospitality and support. The second author is supported by the NSFC (Nos. 11771054, 12072042,91852207), the Sino-German Research Group Project (No. GZ1465), and the National Key Project GJXM92579. It is a pleasure to thank C. Dafermos and M. Slemrod for many useful comments.

摘要/Abstract

摘要： This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws. The basic idea is that the “meaningful objects” are the fluxes, evaluated across domain boundaries over time intervals. The fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional setting. It implies that a weak solution indeed satisfies the balance law. In fact, it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the boundary. It should be emphasized that the weak solutions considered here need not be entropy solutions. Furthermore, the assumption imposed on the flux f(u) is quite minimal—just that it is locally bounded.

关键词: Balance laws, Hyperbolic conservation laws, Multi-dimensional, Discontinuous solutions, Finite-volume schemes, Flux, Trace on boundary

Abstract: This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws. The basic idea is that the “meaningful objects” are the fluxes, evaluated across domain boundaries over time intervals. The fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional setting. It implies that a weak solution indeed satisfies the balance law. In fact, it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the boundary. It should be emphasized that the weak solutions considered here need not be entropy solutions. Furthermore, the assumption imposed on the flux f(u) is quite minimal—just that it is locally bounded.

Key words: Balance laws, Hyperbolic conservation laws, Multi-dimensional, Discontinuous solutions, Finite-volume schemes, Flux, Trace on boundary

中图分类号:

Matania Ben-Artzi, Jiequan Li. Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws[J]. Communications on Applied Mathematics and Computation, 2023, 5(3): 1289-1298.

参考文献

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Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws

Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws

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