Regularized solution of a Cauchy problem for stochastic elliptic equation

Authors: Nguyễn Huy Tuấn, Trần Ngọc Thạch, Yong Zhou, Luu Vu Cam Hoan, Nguyễn Huy Tuấn,

https://onlinelibrary.wiley.com/doi/full/10.1002/mma.6519

Publisher, magazine: ,

Publication year: 2020

  Lưu        Trích dẫn         Chia sẻ

Abstract

In this study, we investigate a Cauchy problem for the stochastic elliptic equation driven by Wiener noise. We show this problem is not well‐posed by proposing a simple illustrative example. To regularize the instable solution, we apply a regularization method called Fourier truncated expansion method. Furthermore, the convergence rate of the regularized solution is also investigated.

Tags: initial value problem, regularized solution, stochastic elliptic equation, the ill-posedness