2 citations · 3 across the 7 of their papers we have counts for
13 papers
Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow
Julian Fischer, Alice Marveggio
Phase-field models such as the Allen-Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scalin…
A monotonicity formula for minimizers of the Mumford-Shah functional in 2d and a sharp lower bound on the energy density
Julian Fischer
We establish a new monotonicity formula for minimizers of the Mumford-Shah functional in planar domains. Our formula follows the spirit of Bucur-Luckhaus, but works with the David-…
Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion
Klemens Fellner, Julian Fischer, Michael Kniely +1
The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to ha…
Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies
Julian Fischer, Tim Laux, Theresa M. Simon
We give a short and self-contained proof for rates of convergence of the Allen-Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter…
A priori error analysis of a numerical stochastic homogenization method
Julian Fischer, Dietmar Gallistl, Daniel Peterseim
This paper provides an a~priori error analysis of a localized orthogonal decomposition method (LOD) for the numerical stochastic homogenization of a model random diffusion problem.…
The waiting time phenomenon in spatially discretized porous medium and thin film equations
Julian Fischer, Daniel Matthes
Various degenerate diffusion equations exhibit a waiting time phenomenon: Dependening on the "flatness" of the compactly supported initial datum at the boundary of the support, the…