Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces. Issue 4 (3rd April 2017)

• Record Type: Journal Article
• Authors: Gal, Ciprian G.; Warma, Mahamadi
• Is Part Of: Communications in partial differential equations. Volume 42:Issue 4(2017)
• Page Start: 579
• Page End: 625
• Publication Date: 2017-04-03
• Subjects: Existence and regularity of solutions -- fractional diffusion -- nonlocal transmission problem -- semilinear parabolic equations; 35R11 -- 35A15 -- 35K55; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2017.1295060
• Languages: English
• ISSNs: 0360-5302

Abstract

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.