Nicola De Nitti

TL;DR: In this article, the authors consider a class of nonlocal conservation laws with a second-order viscous regularization term which finds an application in modelling macroscopic traffic flow and show that, under a suitable balance condition, the solution of the nonlocal problem converges to the entropy solution of corresponding local conservation law.

TL;DR: In this article, the exact boundary controllability of a class of nonlocal conservation laws for traffic flow is studied and the authors show that the boundary control can be used to steer the system towards a target final state or out-flux.

TL;DR: In this paper, the problem of approximating a scalar conservation law by a conservation law with nonlocal flux was studied, and it was shown that the (unique) weak solution of the nonlocal problem converges strongly in O(L √ n) to the entropy solution of local conservation law.

TL;DR: In this paper , the Lagrangian flow of Ambrosio and Smirnov has been studied and the regularity of the flow has been shown to be a regular solution of the continuity equation.

TL;DR: In this article, the authors established sharp criteria for the instantaneous propagation of free boundaries in solutions to the thin-film equation, which are formulated in terms of the initial distribution of mass (as opposed to previous almost-optimal results).