Abstract:
We consider a non-local traffic model involving a convolution product. Unlike other studies, the considered kernel is discontinuous on R. We prove Sobolev estimates and prove the convergence of approximate solutions solving a viscous and regularized non-local equation. It leads to weak, C([0,T],L^2(R)) and C([0,T],L^2(R)), and smooth, W^{2,2N}([0,T]×\R) and W^{2,2N}([0,T]×R), solutions for the non-local traffic model.