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We deal with the problem of approximating a scalar conservation law by aconservation law with nonlocal flux. As convolution kernel in the nonlocalflux, we consider an exponential-type approximation of the Dirac distribution.This enables us to obtain a total variation bound on the nonlocal term. Byusing this, we prove that the (unique) weak solution of the nonlocal problemconverges strongly in $C(L^{1}_{\text{loc}})$ to the entropy solution of thelocal conservation law. We conclude with several numerical illustrations whichunderline the main results and, in particular, the difference between thesolution and the nonlocal term.

A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels