Hamilton-Jacobi equations are first order PDEs of a special type related to the dynamics of a Hamiltonian flow. Weak KAM theory is a set of tools in dynamical systems that enable us to solve these equations using a semi-group of non-linear operators. We will develop in this lecture a discrete-in-time approach and compare this model to the Frenkel-Kontorova model in Solid State Physics. We will also show that the discrete model converges to the continuous model as the time step goes to zero.
University of Bordeaux
Fri, 27/04/2018 - 2:00pm to 3:00pm
RC-4082, The Red Centre, UNSW