Terminal value problem for nonlinear parabolic equation with Gaussian white noise

Autor:	Vinh Quang Mai, Erkan Nane, Donal O'Regan, Nguyen Huy Tuan
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	quasi-reversibility method backward problem parabolic equation gaussian white noise regularization Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Electronic Research Archive, Vol 30, Iss 4, Pp 1374-1413 (2022)
Druh dokumentu:	article
ISSN:	2688-1594
DOI:	10.3934/era.2022072?viewType=HTML
Popis:	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].
Databáze:	Directory of Open Access Journals
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