A remark on duality solutions for some weakly nonlinear scalar   conservation laws
  We investigate existence and uniqueness of duality solutions for a scalar conservation law with a nonlocal interaction kernel. Following the work of Bouchut and James (Comm. Partial Diff. Eq., 24, 1999), a notion of duality solution for such a nonlinear system is proposed, for which we do not have uniqueness. Then we prove that a natural definition of the flux allows to select a solution for which uniqueness holds. 
Fran\c{c}ois James (MAPMO), Nicolas Vauchelet (LJLL, INRIA   Rocquencourt)
math.AP