G.M. Coclite, De Nitti N., Zuazua E.. Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave (2023) CVGMT
Abstract. 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.
arxiv: 00.0000
