The Ghent Methusalem Colloquium is intended for a broad audience of PhD students, postdocs and professors at the Ghent Analysis & PDE Center and beyond. The series includes colloquia from visiting and invited guests.
Prof. Philippe Souplet
Paris Nord, France
Topic: Singularities of solutions of the diffusive Hamilton-Jacobi equation
Time: 16 December 2021
Where: Ghent University
We consider the diffusive Hamilton-Jacobi equation , with homogeneous Dirichlet conditions, which plays an important role in stochastic control theory, as well as in certain models of surface growth (KPZ). Despite its simplicity, it displays, in the surquadratic case , a variety of interesting behaviors and we will discuss two classes of phenomena:
– Gradient blowup (GBU): boundary localisation of singularities, single point point blowup, blowup rates, space and space-time profiles, Liouville type theorems and applications;
– Continuation after GBU as a global viscosity solution: GBU with or without loss of boundary conditions (LBC), recovery of of boundary conditions (RBC) with or without regularisation, multiple time GBU and LBC
In particular, in one space dimension, we will present the, recently obtained, complete classification of GBU and RBC rates and profiles.
Based on a series of joint works with A. Attouchi, R. Filippucci, Y. Li, N. Mizoguchi, A. Porretta, P. Pucci, Q. Zhang.