Seminar series
Fri, 20 May 2022
16:00 - 18:30
Prof. Luis Caffarelli and Prof. Irene Gamba
University of Texas at Austin



Title: Topics on regularity theory for fully non-linear integro-differential equations

Abstract: We will focus on local and non-local Monge Ampere type equations, equations with deforming kernels and convex envelopes of functions with optimal special conditions. We discuss global solutions and their regularity properties.


Title: Quasilinear Conservative Collisional Transport in Kinetic Mean Field models

AbstractWe shall focus the on the interplay of nonlinear analysis  and numerical approximations to mean field models in particle physics where kinetic transport flows in momentum are strongly nonlinearly  modified by macroscopic quantities in classical or spectral density spaces. Two noteworthy models arise: the classical Fokker-Plank Landau dynamics as a low magnetized plasma regimes in the modeling of perturbative non-local high order terms. The other one corresponds to perturbation under strongly magnetized dynamics for fast electrons  in momentum space  give raise to a coupled system of classical kinetic diffusion processes described by the balance equations for electron probability density functions (electron pdf) coupled to the time dynamics on spectral energy waves  (quasi-particles) in a quantum process of their resonant interaction. Both models are rather different, yet there are derived form the Liouville-Maxwell system under different scaling. Analytical tools and some numerical  simulations show a presence of  strong hot tail anisotropy  formation taking the stationary states away from Classical equilibrium solutions stabilization for the iteration in a three dimensional cylindrical model. The semi-discrete schemes preserves the total system mass, momentum and energy, which are enforced by the numerical scheme. Error estimates can be obtained as well.

Work in collaboration with Clark Pennie and Kun Huang

Further Information

Event Timings:

16:00 – 16:10 Refreshments (Served in the North Mezzanine)

16:10 – 17:10  Talk by Prof. Luis Caffarelli

17:10 – 17:30 Refreshments Break (20mins - Served in the North Mezzanine)

17:30 – 18:30 Talk by Prof Irene Martínez Gamba

Each talk will have a Q&A afterwards.

Register your interest HERE

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