422 citations · 2.4k across the 156 of their papers we have counts for
24 papers · 1 filter
Renormalized Invariant Manifolds
Christian Kuehn, Jan-Eric Sulzbach
Invariant manifold theory for partial differential equations (PDEs) is technically challenging as we often lack spectral gaps. Motivated by recent progress using renormalization in…
A dispersive extension result for a class of nonlocal nonlinearities
Bastian Hilder, Christian Kuehn
We prove that a class of nonlocal nonlinearities on periodic Sobolev spaces can be expressed as a trace of the unique mild solution to a local dispersive problem consisting of a sy…
Compatibility of Higher-Order Slow-Manifold Reduction and Continuum Limits in Adaptive Networks
Christian Kuehn, Fergal Murphy, Jan-Eric Sulzbach
Adaptive networks couple the evolution of node states to the evolution of the interactions between them. In fast-adapting phase oscillator networks, a slow-manifold reduction of a…
Thin Domains, Reduction, and Slow Manifolds
Christian Kuehn, Jan-Eric Sulzbach
We propose a unified framework for dimension reduction of partial differential equations posed on thin domains. Our approach combines three complementary ingredients: a careful bou…
Infinite dimensional Slow Manifolds for a Linear Fast-Reaction System
Christian Kuehn, Pascal Lehner, Jan-Eric Sulzbach
The aim of this expository paper is twofold. We start with a concise overview of the theory of invariant slow manifolds for fast-slow dynamical systems starting with the work by Ti…
Mean-Field Limits for Stochastic Interacting Particles on Digraph Measures
Christian Kuehn, Carlos Pulido
Many natural phenomena are effectively described by interacting particle systems, which can be modeled using either deterministic or stochastic differential equations (SDEs). In th…