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Shiduo Qu

Publications and source records attributed to Shiduo Qu.

3 recordsLinked to original sources
arXiv2024

Delay rough evolution equations

In this paper, we accomplish the existence and stability of the solution of a class of delay rough partial differential equations (DRPDEs). Moreover, we prove that the solution of DRPDEs can converge to that of RPDEs in sense of some distance as the delay tends to zero. As applications, we employ the main results to the study of a class of delay stochastic partial differential equations driven by fractional Brownian motion with Hurst parameter $\alpha\in(\frac{1}{3},\frac{1}{2}]$.

math.PR↗
arXiv2023

The high-order approximation of SPDEs with multiplicative noise via amplitude equations

The emphasis of this paper is to investigate the high-order approximation of a class of SPDEs with cubic nonlinearity driven by multiplicative noise with the help of the amplitude equations. The highlight of our work is that we improve the convergence rate between the real solutions and the approximate ones. Precisely, previous results often focused on deriving the approximate solutions via the first-order amplitude equations. However, the approximate solutions are constructed by the first-order amplitude equations and the second-order ones in this paper. And, we rigorously prove that such approximate solutions enjoy improved convergence property. In order to illustrate this demonstration more intuitively, we apply our main theorem to stochastic Allen-Cahn equation, and provide numerical analysis.

math.PR↗