EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

doi:10.1016/S0252-9602(16)30086-8

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (5): 1509-1523.doi: 10.1016/S0252-9602(16)30086-8

EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

Sanjukta DAS, Dwijendra PANDEY, N. SUKAVANAM

Department of Mathematics, Indian Institution of Technology Roorkee, Roorkee, Uttarakhand India

收稿日期:2014-06-23 修回日期:2016-04-25 出版日期:2016-10-25 发布日期:2016-10-25
作者简介:Sanjukta DAS,dassanjukta44@gmail.com;Dwijendra PANDEY,dwij.iitk@gmail.com;N. SUKAVANAM,nsukavanam@gmail.com
基金资助:
The first author was supported by Ministry of Human Resource and Development (MHR-02-23-200-429/304).

EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

Sanjukta DAS, Dwijendra PANDEY, N. SUKAVANAM

Department of Mathematics, Indian Institution of Technology Roorkee, Roorkee, Uttarakhand India

Received:2014-06-23 Revised:2016-04-25 Online:2016-10-25 Published:2016-10-25
Supported by:
The first author was supported by Ministry of Human Resource and Development (MHR-02-23-200-429/304).

摘要/Abstract

摘要：

This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam's novel approach in[22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in[5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in[20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.

关键词: approximate controllability, cosine family, state dependent delay, neutral stochastic differential equation, measure of noncompactness

Abstract:

Key words: approximate controllability, cosine family, state dependent delay, neutral stochastic differential equation, measure of noncompactness

中图分类号:

35R15

Sanjukta DAS, Dwijendra PANDEY, N. SUKAVANAM. EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY[J]. 数学物理学报(英文版), 2016, 36(5): 1509-1523.

Sanjukta DAS, Dwijendra PANDEY, N. SUKAVANAM. EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY[J]. Acta mathematica scientia,Series B, 2016, 36(5): 1509-1523.

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EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

EXISTENCE OF SOLUTION AND APPROXIMATE CONTROLLABILITY OF A SECOND-ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATION WITH STATE DEPENDENT DELAY

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