422 citations · 2.4k across the 156 of their papers we have counts for
4 papers · 2 filters
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…