Related papers: Smoothing of Boundary Behaviour in Stochastic Plan…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
The present article analyses the impact on cosmology, in particular on the evolution of cosmological perturbations, of the existence of extra-dimensions. The model considered here is that of a five-dimensional Anti-de Sitter spacetime where…
We consider a class of semilinear Volterra type stochastic evolution equation driven by multiplicative Gaussian noise. The memory kernel, not necessarily analytic, is such that the deterministic linear equation exhibits a parabolic…
By considering a lattice model of extended phase space, and using techniques of noncommutative differential geometry, we are led to: (a) the conception of vector fields as generators of motion and transition probability distributions on the…
This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the…
We investigate a model of evolutionary dynamics on a smooth landscape which features a ``mutator'' allele whose effect is to increase the mutation rate. We show that the expected proportion of mutators far from equilibrium, when the fitness…
Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing…
Hein and Pr\"{u}ss [J. Differential Equations, 261(2016)4709-4727] presented a version of Hartman-Grobman type $C^{0}$ linearization result for semilinear hyperbolic evolution equations. They showed that the linearising map (homomorphism)…
Smoothed analysis is a framework suggested for mediating gaps between worst-case and average-case complexities. In a recent work, Dinitz et al.~[Distributed Computing, 2018] suggested to use smoothed analysis in order to study dynamic…
The central purpose of the present paper is to study boundary behavior of squeezing functions on bounded domains. We prove that the squeezing function of a strongly pseudoconvex domain tends to 1 near the boundary. In fact, such an estimate…
In the present paper, it was studied the boundary behavior of the so-called lower Q-homeomorphisms in the plane that are a natural generalization of the quasiconformal mappings. In particular, it was found a series of effective conditions…
We study the scaling properties of self-flattening surfaces under global suppression on surface fluctuations. Evolution of self-flattening surfaces is described by restricted solid-on-solid type monomer deposition-evaporation model with…
A class of solid-on-solid growth models with short range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension d=1. Some of the features of the roughening transition which takes place…
In this paper, we study the existence of solutions to sweeping processes in the presence of stochastic perturbations, where the moving set takes uniformly prox-regular values and varies continuously with respect to the Hausdorff distance,…
We prove well-posedness in reflexive Sobolev spaces of weak solutions to the stationary Stokes problem with Navier slip boundary condition over bounded domains $\Omega$ of $\mathbb{R}^n$ of class $W^{2-1/s}_s$, $s>n$. Since such domains are…
The long-time behavior of stochastic Hamilton-Jacobi equations is analyzed, including the stochastic mean curvature flow as a special case. In a variety of settings, new and sharpened results are obtained. Among them are (i) a…
Embryonic development involves pattern formation characterized by the emergence of spatially localized domains characterized by distinct cell fates resulting from differential gene expression. The boundaries demarcating these domains are…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original…
We study proper holomorphic mappings between strictly pseudoconvex domains with low boundary regularity.