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arXiv · 1704.08784

Kinetic solutions for nonlocal scalar conservation laws

Jinlong Wei·Jinqiao Duan·Guangying Lv
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Abstract

This work is devoted to examine the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal super-critical diffusion operator. Our proof for uniqueness is based upon the analysis on a microscopic contraction functional and the existence is enabled by a parabolic approximation. As an illustration, we obtain the existence and uniqueness of kinetic solutions for the generalized fractional Burgers-Fisher type equations. Moreover, we demonstrate the kinetic solutions' Lipschitz continuity in time, and continuous dependence on nonlinearities and L\'{e}vy measures.

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Jinlong Wei, Jinqiao Duan, Guangying Lv. 2017-04-28. Kinetic solutions for nonlocal scalar conservation laws. https://arxiv.org/abs/1704.08784

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