Differ Equ Dyn Syst https://doi.org/10.1007/s12591-018-0407-9 ORIGINAL RESEARCH On Controllability of a Two-Dimensional Network of Ferromagnetic Ellipsoidal Samples Shruti Dubey 1 · Sharad Dwivedi 2 © Foundation for Scientific Research and Technological Innovation 2018 Abstract In this article, we address the problem of stability and controllability of two- dimensional network of ferromagnetic particles of ellipsoidal shapes. The dynamics of magnetization inside the ferromagnetic material is governed by the Landau–Lifschitz equa- tion of micromagnetism which is non-linear and parabolic in nature. The control is the magnetic field generated by a dipole whose position and amplitude can be selected. In the absence of control, first we prove the exponential stability of the relevant configurations of the network. Then, we investigate the controllability by the means of external magnetic field induced by the magnetic dipole. Keywords Ferromagnetic material · Landau–Lifschitz equation · Micromagnetics · Control Mathematics Subject Classification Primary: 93B05 · 35Q93 · 93C10; Secondary: 35K55 Introduction Ferromagnetic materials are nowadays used extensively for the development of modern tech- nological devices such as hard-disks, recording heads, cellular phones and magnetic sensors etc. Due to its sensitive response to the applied magnetic field, ferromagnetic materials play a significant role in the advancement of these devices. From the application point of view, it is essential and yet more challenging to study the magnetic behavior of such materials mainly with respect to its stability and controllability features. B Shruti Dubey sdubey@iitm.ac.in Sharad Dwivedi sharadiitm@gmail.com 1 Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India 2 SRM Research Institute and Department of Mathematics, SRM Institute of Science and Technology, Chennai 603 203, India 123