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We establish existence of partially regular weak solutions for the Landau-Lifshitz equation in three space dimensions for smooth initial data of finite Dirichlet energy. The construction is based onâ€¦ (More)

We consider a complex Ginzburg-Landau equation that contains a SchrÃ¶dinger term and a damping term that is proportional to the time derivative. Given well-prepared initial conditions that correspondâ€¦ (More)

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of GinzburgLandau vortices for sphere-valued maps. In particular we have theâ€¦ (More)

- Barbora BenesovÃ¡, Christof Melcher, Endre SÃ¼li
- SIAM J. Numerical Analysis
- 2014

The paper is concerned with the convergence analysis of a numerical method for nonlocal Cahnâ€“ Hilliard equations. The temporal discretization is based on the implicit midpoint rule and a Fourierâ€¦ (More)

- Christof Melcher
- SIAM J. Math. Analysis
- 2010

We derive a damped wave-type limit for the Landau-Lifshitz-Gilbert equation in thin films starting from the full micromagnetic model. The result, previously encountered in [7] in the context ofâ€¦ (More)

We consider the dynamics of one-dimensional micromagnetic domain walls in layers of uniaxial anisotropy. In the regime of bulk materials, i.e. when the thickness is assumed to be infinite, and theâ€¦ (More)

Most mathematical models for interfaces and transition layers in materials science exhibit sharply localized and rapidly decaying transition profiles. We show that this behavior can largely changeâ€¦ (More)

- Christof Melcher, Mariya Ptashnyk
- SIAM J. Math. Analysis
- 2013

We consider magnetization dynamics under the influence of a spin-polarized current, given in terms of a spin-velocity field v, governed by the following modification of the Landauâ€“ Lifshitzâ€“Gilbertâ€¦ (More)

- Matthias Kurzke, Christof Melcher, Roger Moser
- SIAM J. Math. Analysis
- 2011

We study the Landau-Lifshitz-Gilbert equation for the dynamics of a magnetic vortex system. We include the spin-torque effects of an applied spin current, and rigorously derive an equation of motionâ€¦ (More)

- Fach Mathematik, Von Herrn, +11 authors Lutz Lehmann
- 2008

In this thesis, we are concerned with three classes of non-linear problems that appear naturally in various fields of science, engineering and economics. In order to cover many differentâ€¦ (More)