On Hamilton Jacobi equations with time measurable Hamiltonians posed on a 1-dimensional junction

par Ariela Briani (IDP Tours)

jeudi 12 mars 2026, 14:00 → 15:00 Europe/Paris

E2290 (Tours)

I will study evolutive Hamilton–Jacobi equations with Hamiltonians that are discontinuous in time, posed on a simple network consisting of two edges on the real line connected at a single junction. I will introduce a notion of (flux-limited) viscosity solution for Hamiltonians H_i=H_i(t,x,p), (i=1,2) that are assumed to be only measurable in t. Moreover the flux limiter,  A=A(t), acting at the junction, is not required to be continuous but only in L-infinity.
In the case of convex Hamiltonians, I will prove a comparison principle and establish an existence result via the construction of an  optimal control problem. Generalizations to the nonconvex case and to more general networks will be also discussed.