KINETIC SOLUTIONS FOR NONLOCAL SCALAR CONSERVATION LAWS
KINETIC SOLUTIONS FOR NONLOCAL SCALAR CONSERVATION LAWS
复制标题
非定域标量守恒定律的动力学解
DOI：
10.1137/16m108687x
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发表时间：
2018
影响因子：
2
通讯作者：
Lv Guangying
中科院分区：
文献类型：
--
作者：
Wei Jinlong;Duan Jinqiao;Lv Guangying
本文研究了一类涉及非局部超临界扩散算子的标量守恒律的动力学解的唯一性和存在性。我们的唯一性证明是基于对微观收缩泛函的分析，并通过抛物线近似证明其存在性。作为例证，我们得到了一类广义分数阶Burgers-Fisher型方程动力学解的存在唯一性。此外，我们还证明了动力学解在时间上的Lipschitz连续性，以及对非线性和Levy测度的连续依赖。
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 Levy measures.