In this paper we establish the local and global well-posedness of weak and strong solutions
to second order fractional mean-field SDEs with singular/distribution interaction kernels and …

In this paper, we provide a general framework for investigating McKean-Vlasov stochastic
partial differential equations. We first show the existence of weak solutions by combining the …

The aim of this paper is to provide the analysis result for the partial differential equations
arising from the rigorous derivation of the degenerate parabolic-elliptic Keller-Segel system …

This study addresses the environmental challenges posed by consumerism, evaluating the
impact of Degradation-Resistant Organic Compounds (DROCs), such as fats and oils, on …

A broad class of possibly non-unique generalized kinetic solutions to hyperbolic-parabolic
PDEs is introduced. Optimal regularity estimates in time and space for such solutions to …

In this paper, we present an innovative particle system characterized by moderate
interactions, designed to accurately approximate kinetic flocking models that incorporate …

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 …

We construct a finite element method for the numerical solution of a fractional porous
medium equation on a bounded open Lipschitz polytopal domain $\Omega\subset\mathbb …

In this paper, we present a rigorous derivation of the mean-field limit for a moderately
interacting particle system in $\R^ d $$(d\geq 2) $. For stochastic initial data, we …

We derive quantitative estimates for large stochastic systems of interacting particles
perturbed by both idiosyncratic and environmental noises, as well as singular kernels. We …