Related papers: Time-dependency in hyperbolic Anderson model: Stra…
Using the parametric representation of a chaotic many-body quantum system derived earlier, we calculate explicitly the large-time dependence and asymptotic value of the out-of-time correlator (OTOC) of that system. The dependence on time…
This article revisits the problem of global well-posedness for the generalized parabolic Anderson model on $\mathbb{R}^+\times \mathbb{T}^2$ within the framework of paracontrolled calculus \cite{GIP15}. The model is given by the equation:…
We study the large deviations of time-integrated observables of Markov diffusions that have perfectly reflecting boundaries. We discuss how the standard spectral approach to dynamical large deviations must be modified to account for such…
Stochastic homogenization is achieved for a class of elliptic and parabolic equations describing the lifetime, in large domains, of stationary diffusion processes in random environment which are small, statistically isotropic perturbations…
We consider stochastic dynamics of a particle on a plane in presence of two noises and a confining parabolic potential - an analog of the experimentally-relevant Brownian Gyrator (BG) model. In contrast to the standard BG model, we suppose…
Stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains driven by a multiplicative Gaussian noise are considered. The noise term depends on the unknown velocity and its spatial derivatives. The existence of a martingale…
Consider the parabolic Anderson model $\partial_tu=\frac{1}{2}\partial_x^2u+u\, \eta$ on the interval $[0, L]$ with Neumann, Dirichlet or periodic boundary conditions, driven by space-time white noise $\eta$. Using Malliavin-Stein method,…
This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied in the case of nuclear giant monopole resonances. The problem is spatially unbounded as the resonance state is in the…
The subject of this paper is a generalized Camassa-Holm equation under random perturbation. We first establish local existence and uniqueness results as well as blow-up criteria for pathwise solutions in the Sobolev spaces $H^s$ with…
The optimal time for the controllability of linear hyperbolic systems in one dimensional space with one-side controls has been obtained recently for time-independent coefficients in our previous works. In this paper, we consider linear…
We numerically explore the long-time expansion of a one-dimensional Bose-Einstein condensate in a disorder potential employing the Gross-Pitaevskii equation. The goal is to search for unique signatures of Anderson localization in the…
In this paper, we establish a necessary and sufficient stability condition for a class of two coupled first-order linear hyperbolic partial differential equations. Through a backstepping transform, the problem is reformulated as a stability…
The aim of this paper is to study the $d$-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractional Brownian motion with Hurst parameter $% H\in (0,1)$ in…
The stochastic Gross-Pitaevskii equation is used as a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg Landau equation with a trapping potential and an additive space-time white noise.…
In this paper, we study the stochastic heat equation with a general multiplicative Gaussian noise that is white in time and colored in space. Both regularity and strict positivity of the densities of the solution have been established. The…
This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter 1/4\textless{}H\textless{}1/2 in…
In this article, we address the velocity tracking control problem for a class of stochastic non-Newtonian fluids. More precisely, we consider the stochastic third-grade fluid equation perturbed by infinite-dimensional additive white noise…
We investigate the focusing and defocusing energy-critical stochastic nonlinear Schr\"odinger equation, subject to random perturbations in the form of either additive or multiplicative (Stratonovich) noise. We establish local well-posedness…
We study the temporal formation of quantum mechanical bound states within a one-dimensional attractive square-well potential, by first solving the time-independent Schroedinger equation and then study a time dependent system with an…
In this paper, we consider a general time-inconsistent optimal control problem for a non homogeneous linear system, in which its state evolves according to a stochastic differential equation with deterministic coefficients, when the noise…