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

Yongqiang Fu; Lixu Yan

doi:10.1515/math-2020-0060

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

Yongqiang Fu
, Lixu Yan^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1135-1149
Number of pages	15
Journal	Central European Journal of Mathematics
Volume	18
Issue number	1
DOIs	https://doi.org/10.1515/math-2020-0060
State	Published - 1 Jan 2020

Keywords

fractional Laplacian
optimal control
stochastic system
weak solution

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10.1515/math-2020-0060

Cite this

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title = "Weak solutions and optimal controls of stochastic fractional reaction-diffusion systems",

abstract = "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 Gal{\"e}rkin'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.",

keywords = "fractional Laplacian, optimal control, stochastic system, weak solution",

author = "Yongqiang Fu and Lixu Yan",

note = "Publisher Copyright: {\textcopyright} 2020 Yongqiang Fu and Lixu Yan, published by De Gruyter 2020.",

year = "2020",

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doi = "10.1515/math-2020-0060",

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AU - Fu, Yongqiang

AU - Yan, Lixu

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N2 - 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.

AB - 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.

KW - fractional Laplacian

KW - optimal control

KW - stochastic system

KW - weak solution

UR - https://www.scopus.com/pages/publications/85096334107

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DO - 10.1515/math-2020-0060

M3 - 文章

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SP - 1135

EP - 1149

JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

IS - 1

ER -

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

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