2 citations · 6 across the 12 of their papers we have counts for
13 papers
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…
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…
Energetic Derivation and Geometric Reduction of Reaction-Diffusion Systems with Holling-Type Functional Responses
Jan-Eric Sulzbach
This paper presents an energetic derivation of a class of multi-species reaction-diffusion systems incorporating various functional responses, with a focus on and application to ec…
Approximate Slow Manifolds in the Fokker-Planck Equation
Christian Kuehn, Jan-Eric Sulzbach
In this paper we study the dynamics of a fast-slow Fokker-Planck partial differential equation (PDE) viewed as the evolution equation for the density of a multiscale planar stochas…
Slow Manifolds for PDE with Fast Reactions and Small Cross Diffusion
Laurent Desvillettes, Christian Kuehn, Jan-Eric Sulzbach +2
Multiple time scales problems are investigated by combining geometrical and analytical approaches. More precisely, for fast-slow reaction-diffusion systems, we first prove the exis…
Non-isothermal diffuse interface model for phase transition and interface evolution
Chun Liu, Jan-Eric Sulzbach, Yiwei Wang
In this paper, we derive a thermodynamically consistent non-isothermal diffuse interface model for phase transition and interface evolution involving heat transfer. This model is c…
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…
On a Continuum Model for Random Genetic Drift: A Dynamic Boundary Condition Approach
Chun Liu, Jan-Eric Sulzbach, Yiwei Wang
We propose a new continuum model for random genetic drift by employing a dynamic boundary condition approach. The model can be viewed as a regularized version of the Kimura equatio…
Fast Reactions and Slow Manifolds
Christian Kuehn, Jan-Eric Sulzbach
In this paper we generalize the Fenichel theory for attracting critical/slow manifolds to fast-reaction systems in infinite dimensions. In particular, we generalize the theory of i…
Temperature dependent extensions of the Cahn-Hilliard equation
Francesco De Anna, Chun Liu, Anja Schlömerkemper +1
The Cahn-Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In this paper we focus on the dynamics of these binary media, when t…
Well-Posedness for the Reaction-Diffusion Equation with Temperature in a critical Besov Space
Chun Liu, Jan-Eric Sulzbach
We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from non-equilibrium thermodynamics with the energetic variational approach we obtain a genera…
The Brinkman-Fourier System with Ideal Gas Equilibrium
Chun Liu, Jan-Eric Sulzbach
In this work, we will introduce a general framework to derive the thermodynamics of a fluid mechanical system, which guarantees the consistence between the energetic variational ap…