Gal, Ciprian G.; Warma, Mahamadi Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces. (English) Zbl 1373.35331 Commun. Partial Differ. Equations 42, No. 4, 579-625 (2017). 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. Cited in 33 Documents MSC: 35R11 Fractional partial differential equations 35A15 Variational methods applied to PDEs 35K55 Nonlinear parabolic equations Keywords:existence and regularity of solutions; fractional diffusion; nonlocal transmission problem; semilinear parabolic equations PDFBibTeX XMLCite \textit{C. G. Gal} and \textit{M. Warma}, Commun. Partial Differ. Equations 42, No. 4, 579--625 (2017; Zbl 1373.35331) Full Text: DOI