Weak solutions and optimal controls of stochastic fractional reaction-diffusion systems

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...

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Main Authors: Fu Yongqiang, Yan Lixu
Format: Article
Language:English
Published: De Gruyter 2020-11-01
Series:Open Mathematics
Subjects:
stochastic system
fractional laplacian
weak solution
optimal control
60h15
35a01
47h06
Online Access:https://doi.org/10.1515/math-2020-0060
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spelling doaj-8dfbd9aa5d4c4f47a82073547285ee062021-09-06T19:20:12ZengDe 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
collection DOAJ
language English
format Article
sources DOAJ
author Fu Yongqiang
Yan Lixu
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
author_facet Fu Yongqiang
Yan Lixu
author_sort Fu Yongqiang
title 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_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_sort weak solutions and optimal controls of stochastic fractional reaction-diffusion systems
publisher De Gruyter
series Open Mathematics
issn 2391-5455
publishDate 2020-11-01
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.
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
_version_ 1717777085966057472

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