Persistence and stability of solutions of Hamilton–Jacobi equations

Jean-Paul Penot (1) , Constantin Zalinescu (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 University “Al. I. Cuza” Iasi Faculty of Mathematics

Given a convergent sequence of Hamiltonians (Hn ) and a convergent sequence of initial data (gn ), 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.

Mots clés: asymptotic function; bounded convergence; bounded-Hausdorff convergence; convergence; epiconvergence; Hamilton–Jacobi equation; Mosco convergence; variational con- vergence

Domaines: Equations aux dérivées partielles [math.AP]

Jean-Paul Penot, Constantin Zalinescu. Persistence and stability of solutions of Hamilton–Jacobi equations. 2007. ⟨hal-00175209⟩