@phdthesis{Forster2016,
  author    = {Forster, Johannes},
  title     = {Variational Approach to the Modeling and Analysis of Magnetoelastic Materials},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-147226},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2016},
  abstract  = {This doctoral thesis is concerned with the mathematical modeling of magnetoelastic materials and the analysis of PDE systems describing these materials and obtained from a variational approach. The purpose is to capture the behavior of elastic particles that are not only magnetic but exhibit a magnetic domain structure which is well described by the micromagnetic energy and the Landau-Lifshitz-Gilbert equation of the magnetization. The equation of motion for the material's velocity is derived in a continuum mechanical setting from an energy ansatz. In the modeling process, the focus is on the interplay between Lagrangian and Eulerian coordinate systems to combine elasticity and magnetism in one model without the assumption of small deformations. The resulting general PDE system is simplified using special assumptions. Existence of weak solutions is proved for two variants of the PDE system, one including gradient flow dynamics on the magnetization, and the other featuring the Landau-Lifshitz-Gilbert equation. The proof is based on a Galerkin method and a fixed point argument. The analysis of the PDE system with the Landau-Lifshitz-Gilbert equation uses a more involved approach to obtain weak solutions based on G. Carbou and P. Fabrie 2001.},
  subject      = {Magnetoelastizit{\"a}t},
  language  = {en}
}