相关论文: Fluctuations in 1D stochastic homogenization of ps…
We present stochastic homogenization results for viscous Hamilton-Jacobi equations using a new argument which is based only on the subadditive structure of maximal subsolutions (solutions of the "metric problem"). This permits us to give…
In this paper, we study the rate of convergence in periodic homogenization of scalar ordinary differential equations. We provide a quantitative error estimate between the solutions of a first-order ordinary differential equation with…
Motivated by the fact that in nature almost all phenomena behave randomly in some scales and deterministically in some other scales, we build up a framework suitable to tackle both deterministic and stochastic homogenization problems…
This dissertation discusses the intermitency phenomenon in three models of turbulence, employing analytical and numerical techniques in the analysis of stochastic processes and the probability distributions which they induce. The initial…
We study the behavior of solutions to a Schr{\"o}dinger equation with large, rapidly oscillating, mean zero, random potential with Gaussian distribution. We show that in high dimension $d>\mathfrak{m}$, where $\mathfrak{m}$ is the order of…
We study the problem of characterizing the effective (homogenized) properties of materials whose diffusive properties are modeled with random fields. Focusing on elliptic PDEs with stationary and ergodic random coefficient functions, we…
We study the homogenization problem for a system of stochastic differential equation with local time terms that models a multivariate diffusion in presence of semipermeable hyperplane interfaces with oblique penetration. We show that this…
Dynamical random walk of classical particle in thermodynamically equilibrium fluctuating medium, - Gaussian random potential field, - is considered in the framework of explicit stochastic representation of deterministic interactions. We…
Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framework…
We address the homogenization of a semilinear hyperbolic stochastic partial differential equation with highly oscillating coefficients, in the context of ergodic algebras with mean value. To achieve our goal, we use a suitable variant of…
In this paper, we consider a microscopic semilinear elliptic equation posed in periodically perforated domains and associated with the Fourier-type condition on internal micro-surfaces. The first contribution of this work is the…
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ($L^\infty$) coefficients. Our method does not rely on concepts of ergodicity or…
Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic…
This paper concerns the macroscopic behavior of solutions to parabolic equations with large, highly oscillatory, random potential. When the correlation function of the random potential satisfies a specific integrability condition, we show…
This paper is about the homogenization of linear elliptic operators in divergence form with stationary random coefficients that have only slowly decaying correlations. It deduces optimal estimates of the homogenization error from optimal…
For two scale elliptic equations in a domain $D$, standard homogenization errors are deduced with the assumption that the solution $u_0$ of the homogenized equation belongs to $H^2(D)$. For two scale Maxwell equations, the corresponding…
We study the qualitative homogenization of second order viscous Hamilton-Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient)…
The paper studies solutions of stochastic partial differential equations with random initial conditions. First, it overviews some of the known results on scaled solutions of such equations and provides several explicit motivating examples.…
We consider the homogenization of a semilinear elliptic equation where the coefficients of the second-order differential operator may be discontinuous. We establish the existence and uniqueness of the fine-scale solution, followed by an a…
We propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history-dependent rates. Long-range temporal correlations are seen to alter the speed of the large deviation…