a Laboratoire de Mathématiques appliquées, ERS CNRS 2055, Faculté des sciences, av. de l'Université, 64000 Pau, France b University “Al. I. Cuza” Ia?i, Faculty of Mathematics, Bd. Carol I, Nr. 11, 700506 Ia?i, Romania
Abstract:
Given a convergent sequence of Hamiltonians (Hn) and a convergent sequence of initial data (gn) for the first-order evolutionary Hamilton-Jacobi equation, we look for conditions ensuring that the sequences (un) and (vn) of Lax solutions and Hopf solutions respectively converge. The convergences we deal with are variational convergences. We take advantage of several recent results giving criteria for the continuity of usual operations.