Weak solutions and optimal controls of stochastic fractional reaction-diffusion systems
The aim of this paper is to investigate a class of nonlinear stochastic reaction-diffusion systems involving fractional Laplacian in a bounded domain. First, the existence and uniqueness of weak solutions are proved by using Galërkin’s method. Second, the existence of optimal controls for the corres...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-11-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2020-0060 |
| _version_ | 1818581033284534272 |
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| author | Fu Yongqiang Yan Lixu |
| author_facet | Fu Yongqiang Yan Lixu |
| author_sort | Fu Yongqiang |
| collection | DOAJ |
| description | The aim of this paper is to investigate a class of nonlinear stochastic reaction-diffusion systems involving fractional Laplacian in a bounded domain. First, the existence and uniqueness of weak solutions are proved by using Galërkin’s method. Second, the existence of optimal controls for the corresponding stochastic optimal control problem is obtained. Finally, several examples are provided to demonstrate the theoretical results. |
| first_indexed | 2024-12-16T07:27:03Z |
| format | Article |
| id | doaj.art-8dfbd9aa5d4c4f47a82073547285ee06 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-16T07:27:03Z |
| publishDate | 2020-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-8dfbd9aa5d4c4f47a82073547285ee062022-12-21T22:39:28ZengDe GruyterOpen Mathematics2391-54552020-11-011811135114910.1515/math-2020-0060math-2020-0060Weak solutions and optimal controls of stochastic fractional reaction-diffusion systemsFu Yongqiang0Yan Lixu1Department of Mathematics, Harbin Institute of Technology, Harbin, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin, ChinaThe aim of this paper is to investigate a class of nonlinear stochastic reaction-diffusion systems involving fractional Laplacian in a bounded domain. First, the existence and uniqueness of weak solutions are proved by using Galërkin’s method. Second, the existence of optimal controls for the corresponding stochastic optimal control problem is obtained. Finally, several examples are provided to demonstrate the theoretical results.https://doi.org/10.1515/math-2020-0060stochastic systemfractional laplacianweak solutionoptimal control60h1535a0147h06 |
| spellingShingle | Fu Yongqiang Yan Lixu Weak solutions and optimal controls of stochastic fractional reaction-diffusion systems Open Mathematics stochastic system fractional laplacian weak solution optimal control 60h15 35a01 47h06 |
| title | Weak solutions and optimal controls of stochastic fractional reaction-diffusion systems |
| title_full | Weak solutions and optimal controls of stochastic fractional reaction-diffusion systems |
| title_fullStr | Weak solutions and optimal controls of stochastic fractional reaction-diffusion systems |
| title_full_unstemmed | Weak solutions and optimal controls of stochastic fractional reaction-diffusion systems |
| title_short | Weak solutions and optimal controls of stochastic fractional reaction-diffusion systems |
| title_sort | weak solutions and optimal controls of stochastic fractional reaction diffusion systems |
| topic | stochastic system fractional laplacian weak solution optimal control 60h15 35a01 47h06 |
| url | https://doi.org/10.1515/math-2020-0060 |
| work_keys_str_mv | AT fuyongqiang weaksolutionsandoptimalcontrolsofstochasticfractionalreactiondiffusionsystems AT yanlixu weaksolutionsandoptimalcontrolsofstochasticfractionalreactiondiffusionsystems |