Well-posedness of IBVP for 1D scalar non-local conservation laws

Discretization by means of edge finite elements leads to a system with a new right hand side (Ψ, curl w h ) that belongs to the image of the matrix K, and the curl curl operator

1 Let us observe in passing that in [47,49] the authors established existence and uniqueness of entropy solutions with a combination of u- and x-discontinuities; this approach is

In the context of road traffic modeling we consider a scalar hyperbolic conservation law with the flux (fundamental diagram) which is discontinuous at x = 0, featuring variable

However with an additional control g(t) as in (1.1) and with f (z) = z 2 2 (Burgers equation), Chapouly showed in [9] that in the framework of classical solutions, any state

[1] Gregory R. Baker, Xiao Li, and Anne C. Analytic structure of two 1D-transport equations with nonlocal fluxes. Bass, Zhen-Qing Chen, and Moritz Kassmann. Non-local Dirichlet

Keywords: finite volume scheme, scalar conservation law, non-local point constraint, crowd dynamics, capacity drop, Braess’ paradox, Faster Is Slower.. 2000 MSC: 35L65, 90B20,

The Godunov scheme for scalar conservation laws with discontinuous bell-shaped flux functions.. Boris Andreianov,

exists a unique L ∞ (0, T ; BV (Ω)) entropy solution of the onservation law satisfying (pointwise on Σ ) the BLN boundary ondition; and that this solution is the limit of the