Abstract for the talk on 18.09.2018 (16:45 h)
Oberseminar ANALYSIS - PROBABILITYAndrei Tarfulea (University of Chicago)
Regularity and asymptotics for physical evolution equations
One of the most important areas of applied analysis is in the development
of robust bounds for physically motivated evolution equations. When the
equations feature prominent nonlinear/nonlocal effects (which are
notoriously difficult to handle), such bounds can nevertheless recover
certain asymptotic properties that simplify the problem or even the
equations themselves.
The focus of this lecture will be on recent results for three physical
models: homogenization and asymptotics for nonlocal reaction-diffusion
equations, a priori bounds for hydrodynamic equations with thermal
effects, and the local well-posedness for the Landau equation. Each
problem presents unique challenges arising from the nonlinearity and/or
nonlocality of the equation(s), and the emphasis will be on the different
methods and techniques used to treat these difficulties. The talk will
touch on novelties in viscosity theory and precision in nonlocal front
propagation for reaction-diffusion equations, as well as the emergence of
dynamic self-regularization in the thermal hydrodynamic and Landau
equations.