Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications
This paper derives several well-posedness (existence and uniqueness) and stability results for nonlinear stochastic distributed parameter systems (SDPSs) governed by nonlinear partial differential equations (PDEs) subject to both state-dependent and additive stochastic disturbances. These systems do...
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| Format: | Journal Article |
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The American Society of Mechanical Engineers
2016
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| Online Access: | http://hdl.handle.net/20.500.11937/51405 |
| _version_ | 1848758689894236160 |
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| author | Do, Khac Duc |
| author_facet | Do, Khac Duc |
| author_sort | Do, Khac Duc |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper derives several well-posedness (existence and uniqueness) and stability results for nonlinear stochastic distributed parameter systems (SDPSs) governed by nonlinear partial differential equations (PDEs) subject to both state-dependent and additive stochastic disturbances. These systems do not need to satisfy global Lipschitz and linear growth conditions. First, the nonlinear SDPSs are transformed to stochastic evolution systems (SESs), which are governed by stochastic ordinary differential equations (SODEs) in appropriate Hilbert spaces, using functional analysis. Second, Lyapunov sufficient conditions are derived to ensure well-posedness and almost sure (a.s.) asymptotic and practical stability of strong solutions. Third, the above results are applied to study well-posedness and stability of the solutions of two exemplary SDPSs. |
| first_indexed | 2025-11-14T09:47:59Z |
| format | Journal Article |
| id | curtin-20.500.11937-51405 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:47:59Z |
| publishDate | 2016 |
| publisher | The American Society of Mechanical Engineers |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-514052017-09-13T15:48:11Z Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications Do, Khac Duc This paper derives several well-posedness (existence and uniqueness) and stability results for nonlinear stochastic distributed parameter systems (SDPSs) governed by nonlinear partial differential equations (PDEs) subject to both state-dependent and additive stochastic disturbances. These systems do not need to satisfy global Lipschitz and linear growth conditions. First, the nonlinear SDPSs are transformed to stochastic evolution systems (SESs), which are governed by stochastic ordinary differential equations (SODEs) in appropriate Hilbert spaces, using functional analysis. Second, Lyapunov sufficient conditions are derived to ensure well-posedness and almost sure (a.s.) asymptotic and practical stability of strong solutions. Third, the above results are applied to study well-posedness and stability of the solutions of two exemplary SDPSs. 2016 Journal Article http://hdl.handle.net/20.500.11937/51405 10.1115/1.4033946 The American Society of Mechanical Engineers restricted |
| spellingShingle | Do, Khac Duc Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications |
| title | Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications |
| title_full | Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications |
| title_fullStr | Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications |
| title_full_unstemmed | Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications |
| title_short | Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications |
| title_sort | stability of nonlinear stochastic distributed parameter systems and its applications |
| url | http://hdl.handle.net/20.500.11937/51405 |