Terminal value problem for nonlinear parabolic equation with Gaussian white noise
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 observation...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-03-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022072?viewType=HTML |
| _version_ | 1798030826945904640 |
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| author | Vinh Quang Mai Erkan Nane Donal O'Regan Nguyen Huy Tuan |
| author_facet | Vinh Quang Mai Erkan Nane Donal O'Regan Nguyen Huy Tuan |
| author_sort | Vinh Quang Mai |
| collection | DOAJ |
| description | 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]. |
| first_indexed | 2024-04-11T19:46:32Z |
| format | Article |
| id | doaj.art-f1e11e02aa394aaa94e847ceb5355ac8 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-11T19:46:32Z |
| publishDate | 2022-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-f1e11e02aa394aaa94e847ceb5355ac82022-12-22T04:06:27ZengAIMS PressElectronic Research Archive2688-15942022-03-013041374141310.3934/era.2022072Terminal value problem for nonlinear parabolic equation with Gaussian white noiseVinh Quang Mai 0Erkan Nane1Donal O'Regan2Nguyen Huy Tuan31. Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam2. Department of Mathematics and Statistics, Auburn University, Auburn, USA3. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland4. Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam 5. Faculty of Technology, Van Lang University, Ho Chi Minh City, VietnamIn 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].https://www.aimspress.com/article/doi/10.3934/era.2022072?viewType=HTMLquasi-reversibility methodbackward problemparabolic equationgaussian white noise regularization |
| spellingShingle | Vinh Quang Mai Erkan Nane Donal O'Regan Nguyen Huy Tuan Terminal value problem for nonlinear parabolic equation with Gaussian white noise Electronic Research Archive quasi-reversibility method backward problem parabolic equation gaussian white noise regularization |
| title | Terminal value problem for nonlinear parabolic equation with Gaussian white noise |
| title_full | Terminal value problem for nonlinear parabolic equation with Gaussian white noise |
| title_fullStr | Terminal value problem for nonlinear parabolic equation with Gaussian white noise |
| title_full_unstemmed | Terminal value problem for nonlinear parabolic equation with Gaussian white noise |
| title_short | Terminal value problem for nonlinear parabolic equation with Gaussian white noise |
| title_sort | terminal value problem for nonlinear parabolic equation with gaussian white noise |
| topic | quasi-reversibility method backward problem parabolic equation gaussian white noise regularization |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022072?viewType=HTML |
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