Hyperbolic Conservation Laws, Integral Balance Laws and Regularity of Fluxes

doi:10.1007/s42967-023-00298-2

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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URL: https://www.camc.shu.edu.cn/EN/10.1007/s42967-023-00298-2

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Hyperbolic Conservation Laws, Integral Balance Laws and Regularity of Fluxes

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