一个颗粒流模型中的积分-微分守恒律
An Integro-Differential Conservation Law arising in a Model of Granular Flow
摘要：
研究了一个纯量积分微分守恒律。该方程在文献[2]中首次导出，作为颗粒流的缓慢侵蚀极限。考虑一组更一般的侵蚀函数，研究了标准守恒律理论不能适用的初边值问题。我们构造近似解的分步法，通过重新计算在每个时间步的积分项。先验L^ \infty界和BV估计给出了BV解的收敛性和全局存在性。此外，我们给出了一个适定性分析，表明该解决方案是稳定的L^1相对于初始数据。
英文摘要：
We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for which one can not adapt the standard theory of conservation laws. We construct approximate solutions with a fractional step method, by recomputing the integral term at each time step. A-priori L^\infty bounds and BV estimates yield convergence and global existence of BV solutions. Furthermore, we present a well-posedness analysis, showing that the solutions are stable in L^1 with respect to the initial data.
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