Vitali Vougalter, Vitaly Volpert
Solvability of some integro-differential equations with anomalous diffusion and transport
(217K, pdf)

ABSTRACT.  The article 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.