Rigorous derivation of population cross-diffusion systems from moderately interacting particle systems
Population cross-diffusion systems of Shigesada–Kawasaki–Teramoto type are derived in a
mean-field-type limit from stochastic, moderately interacting many-particle systems for …
mean-field-type limit from stochastic, moderately interacting many-particle systems for …
Rigorous mean-field limit and cross-diffusion
The mean-field limit in a weakly interacting stochastic many-particle system for multiple
population species in the whole space is proved. The limiting system consists of cross …
population species in the whole space is proved. The limiting system consists of cross …
Density fluctuations in weakly interacting particle systems via the dean-kawasaki equation
F Cornalba, J Fischer, J Ingmanns, C Raithel - arXiv preprint arXiv …, 2023 - arxiv.org
The Dean-Kawasaki equation-one of the most fundamental SPDEs of fluctuating
hydrodynamics-has been proposed as a model for density fluctuations in weakly interacting …
hydrodynamics-has been proposed as a model for density fluctuations in weakly interacting …
Cross-diffusion systems with entropy structure
A Jüngel - arXiv preprint arXiv:1710.01623, 2017 - arxiv.org
Some results on cross-diffusion systems with entropy structure are reviewed. The focus is on
local-in-time existence results for general systems with normally elliptic diffusion operators …
local-in-time existence results for general systems with normally elliptic diffusion operators …
Macroscopic behaviour in a two-species exclusion process via the method of matched asymptotics
We consider a two-species simple exclusion process on a periodic lattice. We use the
method of matched asymptotics to derive evolution equations for the two population …
method of matched asymptotics to derive evolution equations for the two population …
Interacting particle approximation of cross-diffusion systems
JA Carrillo, S Guo - arXiv preprint arXiv:2402.05094, 2024 - arxiv.org
We derive a class of multi-species cross-diffusion systems from stochastic interacting
particles. We prove existence of weak solutions of the limiting cross-diffusion system as well …
particles. We prove existence of weak solutions of the limiting cross-diffusion system as well …
Rigorous derivations of diffusion systems from moderately interacting particle models
A Holzinger - 2023 - repositum.tuwien.at
This thesis is concerned with the derivation of certain types of nonlinear partial differential
equations from stochastic interacting particle systems. The underlying methods are within …
equations from stochastic interacting particle systems. The underlying methods are within …
Derivation of a fractional cross-diffusion system as the limit of a stochastic many-particle system driven by Lévy noise
ES Daus, M Ptashnyk, C Raithel - Journal of Differential Equations, 2022 - Elsevier
In this article a fractional cross-diffusion system is derived as the rigorous many-particle limit
of a multi-species system of moderately interacting particles that is driven by Lévy noise. The …
of a multi-species system of moderately interacting particles that is driven by Lévy noise. The …
Varadhan's Decomposition of Shift-Invariant Closed -forms for Large Scale Interacting Systems on the Euclidean Lattice
We rigorously formulate and prove for a relatively general class of interactions Varadhan's
Decomposition of shift-invariant closed $ L^ 2$-forms for a large scale interacting system on …
Decomposition of shift-invariant closed $ L^ 2$-forms for a large scale interacting system on …
Large‐Deviation Principle for Interacting Brownian Motions
I Seo - Communications on Pure and Applied Mathematics, 2017 - Wiley Online Library
We prove the large‐deviation principle for the empirical process in a system of locally
interacting Brownian motions in the nonequilibrium. Such a phenomenon has been proven …
interacting Brownian motions in the nonequilibrium. Such a phenomenon has been proven …