Coclite, Giuseppe MariaDe Nitti, NicolaKeimer, AlexanderPflug, LukasZuazua, Enrique2025-06-062025-06-062023-11-04Coclite, G. M., De Nitti, N., Keimer, A., Pflug, L., & Zuazua, E. (2023). Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave. Nonlinearity, 36(11), 5998-6019. https://doi.org/10.1088/1361-6544/ACF01D0951-771510.1088/1361-6544/ACF01Dhttps://hdl.handle.net/20.500.14454/2964We study the long-time behaviour of the unique weak solution of a nonlocal regularisation 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.eng© 2023 IOP Publishing Ltd & London Mathematical Society35L65Approximation of local conservation lawsBurgers equationEntropy solutionsN-wavesNonlocal conservation lawsNonlocal fluxSource-type solutionsjournal article2025-06-061361-6544