Regularization of the backward stochastic heat conduction problem-Reference-Cited by-同舟云学术

Regularization of the backward stochastic heat conduction problem

Published:2021-12-08 Issue:0 Volume:0 Page:
ISSN:1569-3945
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Tuan Nguyen Huy¹,Lesnic Daniel²,Thach Tran Ngoc³,Ngoc Tran Bao⁴

Affiliation:

1. Division of Applied Mathematics, Science and Technology Advanced Institute, and Faculty of Technology , Van Lang University , Ho Chi Minh City , Vietnam

2. Department of Applied Mathematics , University of Leeds , Leeds LS2 9JT , United Kingdom

3. Department of Mathematics and Computer Science , University of Science ; and Vietnam National University , Ho Chi Minh City , Vietnam

4. Department of Mathematics , Faculty of Science , Nong Lam University , Ho Chi Minh City , Vietnam

Abstract

Abstract In this paper, we study the backward problem for the stochastic parabolic heat equation driven by a Wiener process. We show that the problem is ill-posed by violating the continuous dependence on the input data. In order to restore stability, we apply a filter regularization method which is completely new in the stochastic setting. Convergence rates are established under different a priori assumptions on the sought solution.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2020-0013/pdf

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