Hyperbolic Conservation Laws, Integral Balance Laws and Regularity of Fluxes

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.

Keywords

Balance laws / Hyperbolic conservation laws / Finite volume approximations / Flux regularity / Consistency

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Funding

National Outstanding Youth Science Fund Project of National Natural Science Foundation of China(91852207); National Key Scientific Instrument and Equipment Development Projects of China(GJXM92579); Chinesisch-Deutsche Zentrum fur Wissenschaftsforderung(GZ1465)