Emmanuel Chasseigne - Université de Tours - França

Título:

Ergodic problems for viscous Hamilton-Jacobi equations with inward drift.

Resumo:

This talk is based on a series of papers in collaboration with Naoyuki Ichihara (Tokyo).

I will first give a general overview of ergodic-type problems for viscous Hamilton-Jacobi equations in the whole space. We will also study brifely the associated stochastic control otimization problem as well as the links between the elliptic and parabolic cases.

Then I will focus on the existence of critical (additive) eigenvalues and their qualitative properties depending on the potential/forcing term appearing in the equation.

Finally, I will discuss some more recent advances in presence of an additional inward drift.