66 citations · 149 across the 23 of their papers we have counts for
6 papers · 2 filters
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…
Scaling limit of the homogenization commutator for Gaussian coefficient fields
Mitia Duerinckx, Julian Fischer, Antoine Gloria
Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution operator displays fluctuations around its expectation. The…
Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems
Julian Fischer, Stefan Neukamm
We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone ope…
Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation
Nicola De Nitti, Julian Fischer
We establish sharp criteria for the instantaneous propagation of free boundaries in solutions to the thin-film equation. The criteria are formulated in terms of the initial distrib…
Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model
Julian Fischer, Michael Kniely
In the computation of the material properties of random alloys, the method of "special quasirandom structures" attempts to approximate the properties of the alloy on a finite volum…
Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension
Julian Fischer, Sebastian Hensel
In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension - like, for example, the evolution of oil bubbles in…