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Displaying 201 –
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In this article we prove new results concerning the structure and the stability properties of the global attractor associated with a class of nonlinear parabolic stochastic partial differential equations driven by a standard multidimensional brownian motion. We first use monotonicity methods to prove that the random fields either stabilize exponentially rapidly with probability one around one of the two equilibrium states, or that they set out to oscillate between them. In the first case we can...
In this article we prove new results concerning the
structure and the stability properties of the global attractor associated
with a class of nonlinear parabolic stochastic partial differential equations
driven by a standard multidimensional Brownian motion.
We first use monotonicity methods
to prove that the random fields either stabilize exponentially rapidly with
probability one around one of the two equilibrium states, or that they set out
to oscillate between them. In the first case we can...
A description of the short time behavior of solutions of the Allen–Cahn equation with a smoothened additive noise is presented. The key result is that in the sharp interface limit solutions move according to motion by mean curvature with an additional stochastic forcing. This extends a similar result of Funaki [Acta Math. Sin (Engl. Ser.)15 (1999) 407–438] in spatial dimension n=2 to arbitrary dimensions.
In this paper, we establish a small time large deviation principle (small time asymptotics) for the two-dimensional stochastic Navier–Stokes equations driven by multiplicative noise, which not only involves the study of the small noise, but also the investigation of the effect of the small, but highly nonlinear, unbounded drifts.
We consider a stochastic evolution equation in a separable Hilbert spaces H or in a separable Banach space E with a Hölder continuous perturbation on the drift. We review some recent result about pathwise uniqueness for this equation.
We consider the random vector , where are distinct points of and denotes the stochastic process solution to a stochastic wave equation driven by a noise white in time and correlated in space. In a recent paper by Millet and Sanz–Solé [10], sufficient conditions are given ensuring existence and smoothness of density for . We study here the positivity of such density. Using techniques developped in [1] (see also [9]) based on Analysis on an abstract Wiener space, we characterize the set of...
We consider the random vector , where t > 0, x1,...,xd are
distinct points of
and u denotes the stochastic process solution to a stochastic wave
equation driven by
a noise white in time and correlated in space. In a recent paper by
Millet and Sanz–Solé
[10], sufficient conditions are given ensuring existence and
smoothness of
density for . We study here the positivity of such
density. Using
techniques developped in [1] (see also [9]) based
on Analysis on an
abstract Wiener space, we characterize...
The classical result on singularities for the 3D Navier-Stokes equations says that the -dimensional Hausdorff measure of the set of singular points is zero. For a stochastic version of the equation, new results are proved. For statistically stationary solutions, at any given time , with probability one the set of singular points is empty. The same result is true for a.e. initial condition with respect to a measure related to the stationary solution, and if the noise is sufficiently non degenerate...
We prove the existence and smoothness of density for the solution
of a hyperbolic SPDE with free term coefficients depending on
time, under hypoelliptic non degeneracy conditions. The result
extends those proved in Cattiaux and Mesnager, PTRF123 (2002) 453-483 to an infinite dimensional
setting.
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