Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces. Issue 4 (3rd April 2017) - Gal, Ciprian G.
ABSTRACT: We consider a transmission problem consisting of two semilinear parabolic equations involving fractional diffusion operators of different orders in a general non-smooth setting with emphasis on Lipschitz interfaces and transmission conditions along the interface. We give a unified framework for the existence and uniqueness of strong and mild solutions, and their global regularity properties.