15 citations · 40 across the 7 of their papers we have counts for
4 papers · 1 filter
Reduction Methods in Climate Dynamics -- A Brief Review
Felix Hummel, Peter Ashwin, Christian Kuehn
We review a range of reduction methods that have been, or may be useful for connecting models of the Earth's climate system of differing complexity. We particularly focus on method…
Geometric blow-up of a dynamic Turing instability in the Swift-Hohenberg equation
Felix Hummel, Samuel Jelbart, Christian Kuehn
We present a rigorous analysis of the slow passage through a Turing bifurcation in the Swift-Hohenberg equation using a novel approach based on geometric blow-up. We show that the…
Connecting a direct and a Galerkin approach to slow manifolds in infinite dimensions
Maximilian Engel, Felix Hummel, Christian Kuehn
In this paper, we study slow manifolds for infinite-dimensional evolution equations. We compare two approaches: an abstract evolution equation framework and a finite-dimensional sp…
Slow Manifolds for Infinite-Dimensional Evolution Equations
Felix Hummel, Christian Kuehn
We extend classical finite-dimensional Fenichel theory in two directions to infinite dimensions. Under comparably weak assumptions we show that the solution of an infinite-dimensio…