A numerical method for a backward problem of a linear stochastic Kuramoto-Sivashinsky equation

Abstract

This paper concerns a backward problem for a linear stochastic Kuramoto–Sivashinsky equation, which aims to reconstruct the initial value from the mean measurement at the terminal time. By transforming the backward problem into a regularized optimization one, a regularization method together with its numerical implementation in a finite dimensional space is proposed for solving the backward problem. Finally, we show effectiveness of the proposed reconstruction method by several numerical examples.