Related papers: Well-posedness of diffusion-aggregation equations …
A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…
We introduce a framework to prove propagation of chaos for interacting particle systems with singular, density-dependent interactions, a classical challenge in mean-field theory. Our approach is to define the dynamics implicitly via a…
We consider a Keller-Segel model with non-linear porous medium type diffusion and nonlocal attractive power law interaction, focusing on potentials that are less singular than Newtonian interaction. Here, the nonlinear diffusion is chosen…
In this paper, we investigate the global well-posedness of reaction-diffusion systems with transport noise on the $d$-dimensional torus. We show new global well-posedness results for a large class of scalar equations (e.g. the Allen-Cahn…
We study the well-posedness, steady states and long time behavior of solutions to Vlasov-Fokker-Planck equation with external confinement potential and nonlinear self-consistent interactions. Our analysis introduces newly characterized…
We investigate a model for collective behaviour with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure solutions (defined via mass transport) on sphere, as well as investigate the mean-field particle…
We study the existence and uniqueness of rank-based interacting systems of stochastic differential equations. These systems can be seen as modifications with state-dependent coefficients of the Atlas model in mathematical finance. The…
Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…
This paper is mainly concerned with the large deviation principle of the fractional McKean-Vlasov stochastic reaction-diffusion equation defined on R^n with polynomial drift of any degree. We first prove the well-posedness of the underlying…
We study the boundedness and convergence to equilibrium of weak solutions to reaction-diffusion systems with nonlinear diffusion. The nonlinear diffusion is of porous medium type and the nonlinear reaction terms are assumed to grow…
We prove well-posedness results for time-inhomogeneous stable-driven McKean-Vlasov stochastic differential equations with a convolution drift where the interaction kernel belongs to some Lebesgue-Besov space. The novelty of this work is…
We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise…
Irreversible random sequential deposition of interacting particles is widely used to model aggregation phenomena in physical, chemical, and biophysical systems. We show that in one dimension the exact time dependent solution of such…
For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson…
We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial…
We study a class of McKean--Vlasov Stochastic Differential Equations (MV-SDEs) with drifts and diffusions having super-linear growth in measure and space -- the maps have general polynomial form but also satisfy a certain monotonicity…
In this paper, we investigate the well-posedness of the martingale problem associated to non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under mild assumptions on the coefficients as well as classical…
For finite interacting particle systems with strong repulsing-attracting or general interactions, we prove global weak well-posedness almost up to the critical threshold of the strengths of attracting interactions (independent of the number…