Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces
Ciprian G. Gal, Mahamadi Warma · Communications in Partial Differential Equations · 2017
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.