Harmonic fields and Maxwell equations on perforated domains. (March 2020)

• Record Type: Journal Article
• Authors: Qin, Zengyun
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: 35A15 -- 35J15 -- 35J25 -- 35J50 -- 35J57 -- 35Q61; Elliptic equation -- Harmonic vector field -- The Maxwell equations -- Div–curl system -- Perforated domain; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111663
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the Dirichlet fields and Neumann fields in a perforated domain Ω ε n with n balls of radius ε removed from a simply-connected domain Ω . Structures of these vector fields are obtained. Asymptotic behavior of the solution to the Maxwell equations in the perforated domain is also examined as the number of the holes increases to infinity.