Speaker Bio

Vitali Vougalter is a Canadian mathematician. Vougalter earned his doctorate from Georgia Tech, Atlanta in 2000, under supervision of Michael Loss and Laszlo Erdos. He held a lecturer position at the University of Cape Town. Since 2014 he holds a visiting professor position at the University of Toronto. His research has largely concerned the nonlocal reaction-diffusion equations. In 2020, he received the Afraimovich Award for the Nonlinear Science for his works on this subject.

Abstract:

In the work we establish the existence of solutions of a system of integro-differential equations in the case of the double scale anomalous diffusion. Each equation of the system contains the sum of the two negative Laplace operators raised to two distinct fractional powers in $ R^d, d=4,5$. The proof of the existence of solutions relies on a fixed point technique. We use the solvability conditions for the non-Fredholm elliptic operators in unbounded domains.