Related papers: Exponential decay for the growth-fragmentation/cel…
We study the asymptotic behaviour of a real-valued diffusion whose non-regular drift is given as a sum of a dissipative term and a bounded measurable one. We prove that two trajectories of that diffusion converge a.s. to one another at an…
This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants…
The self-similar growth-fragmentation equation describes the evolution of a medium in which particles grow and divide as time proceeds, with the growth and splitting of each particle depending only upon its size. The critical case of the…
In this paper we determine the exact rate of growth of the solution of a deterministic delay differential equation in which the delayed term is regularly varying at infinity and dominates, and determine criteria to characterise this…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
This paper is devoted to Fokker-Planck and linear kinetic equations with very weak confinement corresponding to a potential with an at most logarithmic growth and no integrable stationary state. Our goal is to understand how to measure the…
We study the exponential decay of relative entropy functionals for zero-range processes on the complete graph. For the standard model with rates increasing at infinity we prove entropy dissipation estimates, uniformly over the number of…
In this paper, hypocoercivity methods are applied to linear kinetic equations with mass conservation and without confinement, in order to prove that the solutions have an algebraic decay rate in the long-time range, which the same as the…
The strong convergence of Euler approximations of stochastic delay differential equations is proved under general conditions. The assumptions on drift and diffusion coefficients have been relaxed to include polynomial growth and only…
The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied. To this end, a rescaled zero-range…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
We establish, in general terms, the conditions to be satisfied by a time-fractional approach formulation of the Poisson-Nernst-Planck model in order to guarantee that the total current across the sample be solenoidal, as required by the…
Exponential stochastic compression is the process when every second cell of an infinite chain may increase its weight merging randomly with left, right, or both neighboring cells. The total mass conservation is assumed. After that, merged…
In this paper, we study the defocusing nonlinear Schr\"{o}dinger equation with a locally distributed damping on a smooth bounded domain as well as on the whole space and on an exterior domain. We first construct approximate solutions using…
We study the asymptotic behavior of a weighted ultrafast diffusion PDE on the real line, with a log-concave and log-lipschitz weight, and prove exponential convergence to equilibrium. This result goes beyond the compact setting studied in…
This paper deals with the exponential stabilization of a time-delay system with an average of the state as the output. A general stability theorem with a guaranteed exponential decay-rate based on a Wirtinger-based inequality is provided.…
We study irreversible dimer nucleation on top of terraces during epitaxial growth in one and two dimensions, for all values of the step-edge barrier. The problem is solved exactly by transforming it into a first passage problem for a random…
In this paper we consider how the statistical moments of the separation between two fluid particles grow with time when their separation lies in the dissipation range of turbulence. In this range the fluid velocity field varies smoothly,…
We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial differential equation with random coefficients that are a perturbation of…
This paper deals with the exponential separation of type II, an important concept for random systems of differential equations with delay, introduced in \JM\ et al.~\cite{MiNoOb1}. Two different approaches to its existence are presented.…