A New Approach for a Nonlocal, Nonlinear Conservation Law

@article{Du2012ANA,
  title={A New Approach for a Nonlocal, Nonlinear Conservation Law},
  author={Qiang Du and James R. Kamm and Richard B. Lehoucq and Michael L. Parks},
  journal={SIAM J. Appl. Math.},
  year={2012},
  volume={72},
  pages={464-487}
}
We describe an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux. The spatially nonlocal operators we consider do not involve derivatives. Instead, the spatial operator involves an integral that, in a distributional sense, reduces to a conventional nonlinear advective operator. In particular, we examine a nonlocal inviscid Burgers equation, which gives a basic form with which to characterize… 

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