Approximate controllability of a class of second order stochastic evolution equations with infinite delay(一类具有无穷时滞的二阶随机发展方程的近似可控性)
This paper presents a study on existence and approximate controllability of the mild solution of a class of second order stochastic evolution equations with infinite delay in Hilbert space. It proves the existence of the mild solution of the studied problem by using the cosine family theory, Hölder...
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Zhejiang University Press
2025-05-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2025.03.011 |
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| author | 强成菊(QIANG Chengju) 范虹霞(FAN Hongxia) |
| author_facet | 强成菊(QIANG Chengju) 范虹霞(FAN Hongxia) |
| author_sort | 强成菊(QIANG Chengju) |
| collection | DOAJ |
| description | This paper presents a study on existence and approximate controllability of the mild solution of a class of second order stochastic evolution equations with infinite delay in Hilbert space. It proves the existence of the mild solution of the studied problem by using the cosine family theory, Hölder inequality, stochastic analysis theory and Mönch fixed point theorem. At the same time, the iterative technique is used to construct the convergent sequence, meanwhile the sufficient condition for the approximate controllability of the problem is obtained by combining the range condition.研究了Hilbert空间中一类具有无穷时滞的二阶随机发展方程。利用余弦族理论、Hölder不等式、随机分析理论和Mönch不动点定理，证明了该方程mild解的存在性；并运用迭代技术构造收敛序列，结合值域型条件，获得了该方程近似可控的充分条件。 |
| format | Article |
| id | doaj-art-aa4286e3b0614c7abb03cdccc811e127 |
| institution | DOAJ |
| issn | 1008-9497 |
| language | zho |
| publishDate | 2025-05-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj-art-aa4286e3b0614c7abb03cdccc811e1272025-08-20T03:03:11ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972025-05-0152338339010.3785/j.issn.1008-9497.2025.03.011Approximate controllability of a class of second order stochastic evolution equations with infinite delay(一类具有无穷时滞的二阶随机发展方程的近似可控性)强成菊(QIANG Chengju)0https://orcid.org/0009-0001-2645-1622范虹霞(FAN Hongxia)1https://orcid.org/0009-0004-0374-8804College of Mathematics and Physics， Lanzhou Jiaotong University， Lanzhou 730070， China(兰州交通大学 数理学院，甘肃 兰州 730070)College of Mathematics and Physics， Lanzhou Jiaotong University， Lanzhou 730070， China(兰州交通大学 数理学院，甘肃 兰州 730070)This paper presents a study on existence and approximate controllability of the mild solution of a class of second order stochastic evolution equations with infinite delay in Hilbert space. It proves the existence of the mild solution of the studied problem by using the cosine family theory, Hölder inequality, stochastic analysis theory and Mönch fixed point theorem. At the same time, the iterative technique is used to construct the convergent sequence, meanwhile the sufficient condition for the approximate controllability of the problem is obtained by combining the range condition.研究了Hilbert空间中一类具有无穷时滞的二阶随机发展方程。利用余弦族理论、Hölder不等式、随机分析理论和Mönch不动点定理，证明了该方程mild解的存在性；并运用迭代技术构造收敛序列，结合值域型条件，获得了该方程近似可控的充分条件。https://doi.org/10.3785/j.issn.1008-9497.2025.03.011 |
| spellingShingle | 强成菊(QIANG Chengju) 范虹霞(FAN Hongxia) Approximate controllability of a class of second order stochastic evolution equations with infinite delay(一类具有无穷时滞的二阶随机发展方程的近似可控性) Zhejiang Daxue xuebao. Lixue ban |
| title | Approximate controllability of a class of second order stochastic evolution equations with infinite delay(一类具有无穷时滞的二阶随机发展方程的近似可控性) |
| title_full | Approximate controllability of a class of second order stochastic evolution equations with infinite delay(一类具有无穷时滞的二阶随机发展方程的近似可控性) |
| title_fullStr | Approximate controllability of a class of second order stochastic evolution equations with infinite delay(一类具有无穷时滞的二阶随机发展方程的近似可控性) |
| title_full_unstemmed | Approximate controllability of a class of second order stochastic evolution equations with infinite delay(一类具有无穷时滞的二阶随机发展方程的近似可控性) |
| title_short | Approximate controllability of a class of second order stochastic evolution equations with infinite delay(一类具有无穷时滞的二阶随机发展方程的近似可控性) |
| title_sort | approximate controllability of a class of second order stochastic evolution equations with infinite delay 一类具有无穷时滞的二阶随机发展方程的近似可控性 |
| url | https://doi.org/10.3785/j.issn.1008-9497.2025.03.011 |
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