We give here an overview of several papers concerning the domain walls dynamics in one-dimensional models of ferromagnetic nanowires. After justifying the one-dimensional models by asymptotic analysis, we first study configurations with one wall in an infinite wire, and we establish the stability of these configurations. In a second part, we prove that the same model in the case of a finite wire is irrelevant because the solution describing one wall is unstable. In addition, it cannot describe complex distributions of several walls located at arbitrary positions. In order to describe such situations, we use Carr and Pego's geometric method to obtain a metastability result for approximate solutions in a model taking into account the smallness of the exchange length.
"Domain walls dynamics in ferromagnetic nanowires." Differential Integral Equations 26 (3/4) 201 - 236, March/April 2013. https://doi.org/10.57262/die/1360092823