Mathematical Analysis of a Class of Surface-Tension Driven Flows
Yuh-Yih Chen
Department of Applied Mathematics, Feng Chia University, Seatwen, Taichung 40724, Taiwan
Jenn-Tsann Lin *
Department of Applied Mathematics, Feng Chia University, Seatwen, Taichung 40724, Taiwan
Hsiu-Chuan Wei
Department of Applied Mathematics, Feng Chia University, Seatwen, Taichung 40724, Taiwan
*Author to whom correspondence should be addressed.
Abstract
In this paper, a two-point boundary value problem arising from a class of surface-tension driven
flows is considered. The existence properties of solutions are established, and all possible solutions
are classified using mathematical analysis. The problem possesses unique or multiple solutions
depending on parameter values. Bifurcation diagrams are computed to verify the results obtained
by mathematical analysis.
Keywords: Similarity solutions, classification, shooting scheme, homogeneity method