| Issue |
ITM Web Conf.
Volume 20, 2018
International Conference on Mathematics (ICM 2018) Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics
|
|
|---|---|---|
| Article Number | 02003 | |
| Number of page(s) | 7 | |
| Section | Numerical and Applied Analysis | |
| DOI | https://doi.org/10.1051/itmconf/20182002003 | |
| Published online | 12 October 2018 | |
A note on inverse problem for strongly damped wave equation with Gaussian white noise
1
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
2
Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
3
Faculty of Applied Science, University of Technology, Ho Chi Minh City, Viet Nam
4
Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam
*
e-mail: chuduckhanh@tdtu.edu.vn
**
e-mail: hoangluctt@gmail.com (corresponding author)
***
e-mail: khanhvanphan@hcmut.edu.vn
****
e-mail: nguyenhuytuan@tdtu.edu.vn
In this paper, we study for the first time the inverse initial problem for the one-dimensional strongly damped wave with Gaussian white noise data. Under some a priori assumptions on the true solution, we propose the Fourier truncation method for stabilizing the ill-posed problem. Error estimates are given in both the L2– and Hp–norms.
Key words: Fourier regularization method / final value problem / strongly damped wave / Gaussian white noise
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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