Calculus of Variations and Geometric Measure Theory

G. M. Coclite - N. De Nitti - A. Keimer - L. Pflug - E. Zuazua

Long-time convergence of a nonlocal Burgers' equation towards the local N-wave

created by denitti on 03 Mar 2023


Submitted Paper

Inserted: 3 mar 2023
Last Updated: 3 mar 2023

Year: 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.