Examinando por Autor "Coclite, Giuseppe Maria"

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    Ítem
    Long-time convergence of a nonlocal Burgers’ equation towards the local N-wave
    (Institute of Physics, 2023-11-04) Coclite, Giuseppe Maria; De Nitti, Nicola; Keimer, Alexander; Pflug, Lukas; Zuazua, Enrique
    We 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.