On stability of steady-statesfor a two-dimensional network model of ferromagnetic nanowires

This article concerns with the mathematical study of stability properties of steady-states for a two-dimensional network model of ferromagnetic nanowires. We consider the finite network model of ferromagnetic nanowires of semi-infinite length. We derive a sufficient condition independent of the size of the network under which the relevant configurations (steady-states) of magnetization are shown to be asymptotically stable. To be precise, we establish the result under certain condition on the length between the two consecutive nanowires. We use perturbation technique and energy method to derive the result.