Related papers: On gradient flow and entropy solutions for nonloca…
The aim of this paper is to prove the existence of multiple solutions for a family of nonlinear elliptic systems in divergence form coupled with a pointwise gradient constraint: \begin{align*} \left\{ \begin{array}{ll}…
We focus on a family of nonlinear continuity equations for the evolution of a non-negative density $\rho$ with a continuous and compactly supported nonlinear mobility $\mathrm{m}(\rho)$ not necessarily concave. The velocity field is the…
Transport properties of a charged droplet of weakly interacting particles in an external field are investigated. A non-equilibrium distribution function which describes a process of the droplet transverse evolution with constant entropy in…
In recent work [1] we uncovered intriguing connections between Otto's characterisation of diffusion as entropic gradient flow [16] on one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other.…
This paper investigates the gradient flow structure, well-posedness, and asymptotic behavior of the Fokker-Planck equation defined on locally uniformly finite graphs, which is highly non-trivial compared with the finite case. We first…
In this paper, we are concerned with the quantification of uncertainties that arise from intra-day oscillations in the demand for natural gas transported through large-scale networks. The short-term transient dynamics of the gas flow is…
We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
We investigate a scalar partial differential equation model for the formation of biological transportation networks. Starting from a discrete graph-based formulation on equilateral triangulations, we rigorously derive the corresponding…
We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with Lagrange multipliers and a set of nonlinear constraints that…
In this paper, we derive a periodic model from a one dimensional nonlocal eikonal equation set on the full space modeling dislocation dynamics. Thanks to a gradient entropy estimate, we show that this periodic model converges toward the…
A relaxed notion of displacement convexity is defined and used to establish short time existence and uniqueness of Wasserstein gradient flows for higher order energy functionals. As an application, local and global well-posedness of…
We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds and exponential stability of discrete approximations…
We present a detailed study of the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system under consideration is a…
Here we study the abstract nonlinear differential equation of second order that in special case is the equation of the type of equation of traffic flow. We prove the solvability theorem for the posed problem under the appropriate conditions…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…
We investigate a mathematical theory for the erosion of sediment which begins with the study of a non-linear, parabolic, weighted 4-Laplace equation on a rectangular domain corresponding to a base segment of an extended landscape. Imposing…
Transport of spherical Brownian particles of finite size possessing radii through narrow channels with varying cross-section area is considered. Applying the so-called Fick-Jacobs approximation, i.e. assuming fast equilibration in…
The present work concerns the derivation of a numerical scheme to approximate weak solutions of the Euler equations with a gravitational source term. The designed scheme is proved to be fully well-balanced since it is able to exactly…
In this paper we give a description of the asymptotic behavior, as $\epsilon\to 0$, of the $\epsilon$-gradient flow in the finite dimensional case. Under very general assumptions we prove that it converges to an evolution obtained by…