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Regularized solution of a Cauchy problem for stochastic elliptic equation
Journal article   Peer reviewed

Regularized solution of a Cauchy problem for stochastic elliptic equation

Tuan Nguyen Huy, Luu Vu Cam Hoan, Yong Zhou and Tran Ngoc Thach
Mathematical methods in the applied sciences, Vol.44(15), pp.11863-11872
10/2021
DOI: https://doi.org/10.1002/mma.6519

Abstract

initial value problem regularized solution stochastic elliptic equation the ill‐posedness
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.

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