Related papers: Approximations to the Stochastic Burgers Equation
We consider the Burgers equation on $H=L^2(0,1)$ perturbed by white noise and the corresponding transition semigroup $P_t$. We prove a new formula for $P_tD\varphi$ (where $\varphi:H\to\R$ is bounded and Borel) which depends on $\varphi$…
We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an…
The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L\'evy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity…
We consider the effect of replacing in stochastic differential equations leading to the dynamical collapse of the statevector, white noise stochastic processes with non white ones. We prove that such a modification can be consistently…
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…
We introduce the uniqueness, existence, $L_p$-regularity, and maximal H\"older regularity of the solution to semilinear stochastic partial differential equation driven by a multiplicative space-time white noise: $$ u_t = au_{xx} + bu_{x} +…
This paper focuses on investigating the density convergence of a fully discrete finite difference method when applied to numerically solve the stochastic Cahn--Hilliard equation driven by multiplicative space-time white noises. The main…
We prove the existence and uniqueness of invariant measures for the fractional stochastic Burgers equation (FSBE) driven by fractional power of the Laplacian and space-time white noise. We show also that the transition measures of the…
The stochastic PDE known as the Kardar-Parisi-Zhang equation (KPZ) has been proposed as a model for a randomly growing interface. This equation can be reformulated as a stochastic Burgers equation. We study a stochastic KdV-Burgers equation…
This article deals with stochastic partial differential equations with quadratic nonlinearities perturbed by small additive and multiplicative noise. We present the approximate solution of the original equation via the amplitude equation…
In this work, we consider the stochastic Burgers-Huxley equation perturbed by multiplicative Gaussian noise, and discuss about the global solvability results and asymptotic behavior of solutions. We show the existence of a global strong…
We study the stochastic Burgers equation driven by an additive Hermite sheet of order $q \ge 1$. The equation is formulated in the mild sense using the heat semigroup, and existence and uniqueness of solutions are established via a…
This study is motivated by the question of how singularity formation and other forms of extreme behavior in nonlinear dissipative partial differential equations are affected by stochastic excitations. To address this question we consider…
We study stochastic Burgers equation driven by a rough noise $(-\Delta)^{\gamma} dW_t$, where $\Delta$ is the Laplacian in one dimension with Dirichlet boundary conditions, and $\gamma \in [0,1/4)$. We prove exponential estimates for the…
In this paper, we consider the averaging principle for one dimensional stochastic Burgers equation with slow and fast time-scales. Under some suitable conditions, we show that the slow component strongly converges to the solution of the…
The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the…
This paper is an introduction to the theory of 1d stochastic Burgers equation under periodic boundary conditions and with a stochastic force, sufficiently smooth in the space variable. We prove the classical results on the existence and…
The present work deals with the global solvability as well as absolute continuity of the law of the solution to stochastic generalized Burgers-Huxley (SGBH) equation driven by multiplicative space-time white noise in a bounded interval of…
The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise, which possesses both Burgers-type and cubic nonlinearities. To discretize the…
We study strictly parabolic stochastic partial differential equations on $\R^d$, $d\ge 1$, driven by a Gaussian noise white in time and coloured in space. Assuming that the coefficients of the differential operator are random, we give…