A bounded dynamical network of curves and the stability of its steady states

Abstract

In this article, we study the dynamic behavior of a network that consists of curves that are in motion and bounded. We first focus on the construction of the model which is a system of nonlinear partial differential equations (PDEs). This system is subject to four conditions: angle and intersection conditions between the curves at the point that they meet and angle and intersection conditions between the curves and the boundary from which the network is bounded. Then, we define a linear operator and study the stability of the steady states of the corresponding boundary value problem (BVP).