Inserted: 3 mar 2023
Last Updated: 3 mar 2023
We study the long-time behavior of the unique weak solution of a nonlocal regularization of the (inviscid) Burgers' equation where the velocity is approximated by a one-sided convolution with an exponential kernel. The initial datum is assumed to be positive, bounded, and integrable. The asymptotic profile is given by the "$N$-wave'' entropy solution of the Burgers' equation. The key ingredients of the proof are a suitable scaling argument and a nonlocal Oleinik-type estimate.