×

Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces. (English) Zbl 1373.35331

Summary: 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.

MSC:

35R11 Fractional partial differential equations
35A15 Variational methods applied to PDEs
35K55 Nonlinear parabolic equations
PDFBibTeX XMLCite
Full Text: DOI