Dec / 2018
04

Dec / 2018
04

Nov / 2018
27

Nov / 2018
27

Homogenization of a class of one-dimensional nonconvex viscous Hamilton-Jacobi equations with random potential

I will present joint work with Elena Kosygina and Ofer Zeitouni in which we prove the homogenization of a class of one-dimensional viscous Hamilton-Jacobi equations with random Hamiltonians that are nonconvex in the gradient variable. Due to the special form of the Hamiltonians, the solutions of these PDEs with linear initial conditions have representations involving exponential expectations of controlled Brownian motion in a random potential. The effective Hamiltonian is the asymptotic rate of growth of these exponential expectations as time goes to infinity and is explicit in terms of the tilted free energy of (uncontrolled) Brownian motion in a random potential. The proof involves large deviations, construction of correctors which lead to exponential martingales, and identification of asymptotically optimal policies.

Nov / 2018
20

Pontifical Catholic University of Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

Faculty of Physical and Mathematical Sciences (FCFM)

Universidad de Chile

Beauchef 851, Edificio Norte, Piso 7,

Santiago – Chile