Approximation of mild solutions of a semilinear fractional differential equation with random noise
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- by Nguyen Huy Tuan, Erkan Nane, Donal O’Regan and Nguyen Duc Phuong PDF
- Proc. Amer. Math. Soc. 148 (2020), 3339-3357 Request permission
Abstract:
We study for the first time the Cauchy problem for semilinear fractional elliptic equations with random data. This paper is concerned with the Gaussian white noise model for initial Cauchy data. We establish the ill-posedness of the problem. Then we propose the Fourier truncation method for stabilizing the ill-posed problem. Some convergence rates between the exact solution and the regularized solution is established in $L^2$ and $H^q$ norms.References
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Additional Information
- Nguyen Huy Tuan
- Affiliation: Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
- MR Author ID: 777405
- ORCID: 0000-0002-6962-1898
- Email: nguyenhuytuan@tdtu.edu.vn
- Erkan Nane
- Affiliation: Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36849
- MR Author ID: 782700
- Email: nane@auburn.edu
- Donal O’Regan
- Affiliation: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
- MR Author ID: 132880
- Email: donal.oregan@nuigalway.ie
- Nguyen Duc Phuong
- Affiliation: Department of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam; and Vietnam National University, Ho Chi Minh City, Vietnam
- MR Author ID: 1332494
- ORCID: 0000-0003-3779-197X
- Email: nducphuong@gmail.com
- Received by editor(s): December 15, 2018
- Received by editor(s) in revised form: November 22, 2019
- Published electronically: April 16, 2020
- Additional Notes: This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2019.09.
The first author is the corresponding author. - Communicated by: Wenxian Shen
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 3339-3357
- MSC (2010): Primary 35R11, 26A33, 45A05, 65J08
- DOI: https://doi.org/10.1090/proc/15029
- MathSciNet review: 4108842