Scientific 鈥淓stimates of the fundamental solution for the stationary convection-diffusion equation鈥�
20 October at 12:00 MSK
We will talk about methods for obtaining estimates for the Green's function and the fundamental solution for the convection-diffusion equation with a uniformly elliptic leading part in the space R^n, n> 2. The goal is to find a sufficient (in a sense close to the necessary one) condition for drift (velocity field) b(x), which gives standard Newtonian estimates for the fundamental solution. The simplest condition of this kind is the boundedness of the drift b(x) with the estimate |b(x)|<|x|^{-1}g(|x|), where g is a nonincreasing function satisfying the Dini condition at infinity (that is, the summability at infinity of the function g(s) s^{- 1}).
Speaker
Professor Surnachev Mikhail D., Keldysh Institute of Applied Mathematics (Russian Academy of Sciences).
Topic: Estimates of the fundamental solution for the stationary convection-diffusion equation.