Bifurcation and stability for charged drops

Article type: Research Article

Authors: Dai, Guowei^{a; *} | Duan, Ben^b | Liu, Fang^c

Affiliations: [a] School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P.R. China | [b] School of Mathematics, Jilin University, Changchun, 130012, P.R. China | [c] School of Information Engineering, Dalian University, Dalian, 116622, P.R. China

Correspondence: [*] Corresponding author. E-mail: daiguowei@dlut.edu.cn.

Abstract: In this paper, we investigate the Laplace’s equation for the electrical potential of charge drops on exterior domain, and overdetermined boundary conditions are prescribed. We determine the local bifurcation structure with respect to the surface tension coefficient as bifurcation parameter. Furthermore, we establish the stability and the instability near the bifurcation point.

Keywords: Bifurcation, stability, charged drops

DOI: 10.3233/ASY-231853

Journal: Asymptotic Analysis, vol. 134, no. 3-4, pp. 575-588, 2023