Examinando por Autor "De Nitti, Nicola"

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  • Miniatura
    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.
  • Miniatura
    Ítem
    On the controllability of entropy solutions of scalar conservation laws at a junction via Lyapunov methods
    (Springer, 2023-01-04) De Nitti, Nicola ; Zuazua, Enrique
    In this note, we prove a controllability result for entropy solutions of scalar conservation laws on a star-shaped graph. Using a Lyapunov-type approach, we show that, under a monotonicity assumption on the flux, if u and v are two entropy solutions corresponding to different initial data and same in-flux boundary data (at the exterior nodes of the star-shaped graph), then u ≡ v for a sufficiently large time. In order words, we can drive u to the target profile v in a sufficiently large control time by inputting the trace of v at the exterior nodes as in-flux boundary data for u. This result can also be shown to hold on tree-shaped networks by an inductive argument. We illustrate the result with some numerical simulations.