arXiv subjects

Guang-an Zou

Publications and source records attributed to Guang-an Zou.

6 recordsLinked to original sources

arXiv2020

Noise and Stability in Reaction-diffusion Equations

We study the stability of reaction-diffusion equations in presence of noise. The relationship of stability of solutions between the stochastic ordinary different equations and the corresponding stochastic reaction-diffusion equation is firstly established. Then, by using the Lyapunov method, sufficient conditions for mean square and stochastic stability are given. The results show that the multiplicative noise can make the solution stable, but the additive noise will be not.

math.PR↗

arXiv2018

A Galerkin finite element method for time-fractional stochastic heat equation

In this study, a Galerkin finite element method is presented for time-fractional stochastic heat equation driven by multiplicative noise, which arises from the consideration of heat transport in porous media with thermal memory with random effects. The spatial and temporal regularity properties of mild solution to the given problem under certain sufficient conditions are obtained. Numerical techniques are developed by the standard Galerkin finite element method in spatial direction, and Gorenflo-Mainardi-Moretti-Paradisi scheme is applied in temporal direction. The convergence error estimates for both semi-discrete and fully discrete schemes are established. Finally, numerical example is provided to verify the theoretical results.

math.NA↗

arXiv2018

Finite difference/element method for time-fractional Navier-Stokes equations

We apply a composite idea of semi-discrete finite difference approximation in time and Galerkin finite element method in space to solve the Navier-Stokes equations with Caputo derivative of order 0 < α < 1. The stability properties and convergence error estimates for both the semi-discrete and fully discrete schemes are obtained. Numerical example is provided to illustrate the validity of theoretical results.

math.NA↗

arXiv2017

Stochastic Navier-Stokes equations with Caputo derivative driven by fractional noises

In this paper, we consider the extended stochastic Navier-Stokes equations with Caputo derivative driven by fractional Brownian motion. We firstly derive the pathwise spatial and temporal regularity of the generalized Ornstein-Uhlenbeck process. Then we discuss the existence, uniqueness, and Hölder regularity of mild solutions to the given problem under certain sufficient conditions, which depend on the fractional order $α$ and Hurst parameter $H$. The results obtained in this study improve some results in existing literature.

math.NA↗

arXiv2017

Stochastic Burgers equation with fractional derivative driven by multiplicative noise

This article is devoted to the study of the existence and uniqueness of mild solution to time- and space-fractional stochastic Burgers equation perturbed by multiplicative white noise. The required results are obtained by stochastic analysis techniques, fractional calculus and semigroup theory. We also proved the regularity properties of mild solution for this generalized Burgers equation.

math.NA↗

arXiv2016

On the study of stochastic fractional-order differential equation systems

In this article, the existence and uniqueness about the solution for a class of stochastic fractional-order differential equation systems are investigated, where the fractional derivative is described in Caputo sense. The fractional calculus, stochastic analysis techniques and the standard Picard's iteration are used to obtain the required results, the nonlinear term is satisfied with some non-Lipschitz conditions (where the classical Lipschitz conditions are special cases). The stochastic fractional-order Newton-Leipnik and Lorenz systems are provided to illustrate the obtained theory, and numerical simulation results are also given by the modified Adams predictor-corrector scheme.

math.NA↗