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arXiv · 1607.08851

Approximate solutions of scalar conservation laws

Misha Perepelitsa
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Abstract

We study compactness properties of time-discrete and continuous time BGK-type schemes for scalar conservation laws, in which microscopic interactions occur only when the state of a system deviates significantly from an equilibrium distribution. The threshold deviation, $\epsilon,$ is a parameter of the problem. In the vanishing relaxation time limit we obtain solutions of a conservation law in which flux is pointwisely close (of order $\epsilon$) to the flux of the original equation and derive several other properties of such solutions, including an example of approximate solution to a shock for Burger's equation.

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Misha Perepelitsa. 2016-07-29. Approximate solutions of scalar conservation laws. https://arxiv.org/abs/1607.08851

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