Title: Well-posedness and error estimates for coupled systems of nonlocal conservation laws Show Chinese title

Title: 适定性及非局部守恒律耦合系统的误差估计

Abstract: This article deals with the error estimates for numerical approximations of the entropy solutions of coupled systems of nonlocal hyperbolic conservation laws. The systems can be strongly coupled through the nonlocal coefficient present in the convection term. A fairly general class of fluxes is being considered, where the local part of the flux can be discontinuous at infinitely many points, with possible accumulation points. The aims of the paper are threefold: 1. Establishing existence of entropy solutions with rough local flux for such systems, by deriving a uniform BV bound on the numerical approximations; 2. Deriving a general Kuznetsov-type lemma (and hence uniqueness) for such systems with both smooth and rough local fluxes; 3. Proving the convergence rate of the finite volume approximations to the entropy solutions of the system as $1/2$ and $1/3$, with homogeneous (in any dimension) and rough local parts (in one dimension), respectively. Numerical experiments are included to illustrate the convergence rates. Show Chinese abstract

Abstract: 本文讨论了耦合非局部双曲守恒律系统的熵解的数值近似误差估计。 系统可以通过对流项中的非局部系数而强烈耦合。 考虑了一类相当广泛的通量，其中通量的局部部分可以在无限多个点上不连续，且可能存在累积点。 本文的目标有三个：1. 通过推导数值近似的一致BV界，建立具有粗糙局部通量的此类系统的熵解的存在性；2. 为具有光滑和粗糙局部通量的此类系统推导一个一般的Kuznetsov型引理（从而得到唯一性）；3. 证明有限体积近似在$1/2$和$1/3$的情况下，分别以均匀（在任何维数）和粗糙局部部分（在一维中）收敛到系统熵解的收敛速率。 包含数值实验以说明收敛速率。