Related papers: Noisy Kuramoto-Sivashinsky equation for an erosion…
We study stochastic evolution equations driven by Gaussian noise. The key features of the model are that the operators in the deterministic and stochastic parts can have the same order and the noise can be time-only, space-only, or…
We present a method for the nonparametric estimation of the drift function of certain types of stochastic differential equations from the empirical density. It is based on a variational formulation of the Fokker-Planck equation. The…
We study the small-mass limit, also known as the Smoluchowski-Kramers diffusion approximation (see \cite{kra} and \cite{smolu}), for a system of stochastic damped wave equations, whose solution is constrained to live in the unitary sphere…
We consider the Kuramoto-Sakaguchi-Fokker-Planck equation (namely, parabolic Kuramoto-Sakaguchi, or Kuramoto-Sakaguchi equation, which is a nonlinear parabolic integro-differential equation) with inertia and white noise effects. We study…
We consider the Langevin equation with multiplicative noise term which depends on time and space. The corresponding Fokker-Planck equation in Stratonovich approach is investigated. Its formal solution is obtained for an arbitrary…
We study the convergence of a Zakharov system driven by a time white noise, colored in space, to a multiplicative stochastic nonlinear Schr{\"o}dinger equation, as the ion-sound speed tends to infinity. In the absence of noise, the…
In this work, we study the 1D stabilized Kuramoto Sivashinsky equation with additive uncorrelated stochastic noise. The Eckhaus stable band of the deterministic equation collapses to a narrow region near the center of the band. This is…
We consider systems of damped wave equations with a state-dependent damping coefficient and perturbed by a Gaussian multiplicative noise. Initially, we investigate their well-posedness, under quite general conditions on the friction.…
All complex fluid motions, such as transition and turbulence, obeying the Navier-Stokes equations are non-linear phenomena. Some aspects of the non-linear terms of these equations are not well understood and are, in fact, misunderstood. The…
Covariance of the resulting probabilities requires the "anti-Ito" sense. The corresponding Fokker-Planck equation is simplified and preserves important features of the case with a constant diffusion. Multiplicative noise can always be…
This paper presents a finite difference method combined with the Crank--Nicolson scheme of the Kuramoto--Sivashinsky equation defined on an expanding circle (\cite{KUY}), and the existence, uniqueness, and second-order error estimate of the…
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by…
We estimate nonparametrically the spatially varying diffusivity of a stochastic heat equation from observations perturbed by additional noise. To that end, we employ a two-step localization procedure, more precisely, we combine local state…
We study the Cauchy problem for Schr\"odinger type stochastic partial differential equations with uniformly bounded coefficients on a curved space. We give conditions on the coefficients, on the drift and diffusion terms, on the Cauchy…
We consider the (noisy) Kuramoto model, that is a population of N oscillators, or rotators, with mean-field interaction. Each oscillator has its own randomly chosen natural frequency (quenched disorder) and it is stirred by Brownian motion.…
A stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated. The drift is assumed only integrable to a certain power. Opposite to the deterministic case where smooth initial…
We analyse a nonlinear stochastic partial differential equation that corresponds to a viscous shallow water equation (of the Camassa--Holm type) perturbed by a convective, position-dependent noise term. We establish the existence of weak…
We present the global-in-time existence of strong solutions and its large-time behavior for the Kuramoto-Sakaguchi equation with inertia. The equation describes the evolution of the probability density function for a large ensemble of…
We present a new stochastic differential equation model for the spontaneous emission noise and carrier noise in semiconductor lasers. The correlations between these two types of noise have often been neglected in recent studies of the…
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…