Solvability of some integro-differential equations with anomalous diffusion and transport

Analysis Seminar
Wednesday, February 24, 2021 - 2:00pm for 1 hour (actually 50 minutes)
Vitali Vougalter – University of Toronto
Benjamin Jaye

The work deals with the existence of solutions of an integro-differential equation in the case of the anomalous diffusion with the negative Laplace operator in a fractional power in the presence of the transport term. The proof of existence of solutions is based on a fixed point technique. Solvability conditions for elliptic operators without Fredholm property in unbounded domains are used. We discuss how the introduction of the transport term impacts the regularity of solutions.