@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}
}
@misc{Forster2013,
  type      = {Master Thesis},
  author    = {Forster, Johannes},
  title     = {Mathematical Modeling of Complex Fluids},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-83533},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2013},
  abstract  = {This thesis gives an overview over mathematical modeling of complex fluids with the discussion of underlying mechanical principles, the introduction of the energetic variational framework, and examples and applications. The purpose is to present a formal energetic variational treatment of energies corresponding to the models of physical phenomena and to derive PDEs for the complex fluid systems. The advantages of this approach over force-based modeling are, e.g., that for complex systems energy terms can be established in a relatively easy way, that force components within a system are not counted twice, and that this approach can naturally combine effects on different scales. We follow a lecture of Professor Dr. Chun Liu from Penn State University, USA, on complex fluids which he gave at the University of Wuerzburg during his Giovanni Prodi professorship in summer 2012. We elaborate on this lecture and consider also parts of his work and publications, and substantially extend the lecture by own calculations and arguments (for papers including an overview over the energetic variational treatment see [HKL10], [Liu11] and references therein).},
  subject      = {Variationsrechnung},
  language  = {en}
}