15 citations · 40 across the 7 of their papers we have counts for
9 papers
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…
Geometric analysis of fast-slow PDEs with fold singularities via Galerkin discretisation
Maximilian Engel, Felix Hummel, Christian Kuehn +3
We study a singularly perturbed fast-slow system of two partial differential equations (PDEs) of reaction-diffusion type on a bounded domain via Galerkin discretisation. We assume…
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…
Sample Paths of White Noise in Spaces with Dominating Mixed Smoothness
Felix Hummel
The sample paths of white noise are proved to be elements of certain Besov spaces with dominating mixed smoothness. Unlike in isotropic spaces, here the regularity does not get wor…
Boundary Value Problems of Elliptic and Parabolic Type with Boundary Data of Negative Regularity
Felix Hummel
We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary…
Elliptic and Parabolic Boundary Value Problems in Weighted Function Spaces
Felix Hummel, Nick Lindemulder
In this paper we study elliptic and parabolic boundary value problems with inhomogeneous boundary conditions in weighted function spaces of Sobolev, Bessel potential, Besov and Tri…
Dispersive mixed-order systems in -Sobolev spaces and application to the thermoelastic plate equation
Robert Denk, Felix Hummel
We study dispersive mixed-order systems of pseudodifferential operators in the setting of -Sobolev spaces. Under the weak condition of quasi-hyperbolicity, these operators gen…