Abstract for the talk on 18.09.2018 (16:45 h)

Oberseminar ANALYSIS - PROBABILITY

Andrei Tarfulea (University of Chicago)
Regularity and asymptotics for physical evolution equations
18.09.2018, 16:45 h, MPI für Mathematik in den Naturwissenschaften Leipzig, A3 01 (Sophus-Lie-SR)

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.

 

03.09.2018, 08:24