@article{Mai2022, 
author = {Vinh Quang Mai and Erkan Nane and Donal O'Regan and Nguyen Huy Tuan},
title = {Terminal value problem for nonlinear parabolic equation with Gaussian white noise},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {4},
pages = {1374-1413},
keywords = {parabolic equation, Quasi-reversibility method, backward problem, Gaussian white noise regularization},
url = {https://www.sciopen.com/article/10.3934/era.2022072},
doi = {10.3934/era.2022072},
abstract = {In this paper, We are interested in studying the backward in time problem for nonlinear parabolic equation with time and space independent coefficients. The main purpose of this paper is to study the problem of determining the initial condition of nonlinear parabolic equations from noisy observations of the final condition. The final data are noisy by the process involving Gaussian white noise. We introduce a regularized method to establish an approximate solution. We establish an upper bound on the rate of convergence of the mean integrated squared error. This article is inspired by the article by Tuan and Nane [1].}
}