Stability Analysis of Second-Order Linear PDEs on Time Scales
This paper presents the stability analysis of a class of second-order linear partial differential equations (PDEs) on time scales with diffusion operator and first-order partial derivative. According to the time scale theory, the Lyapunov functional method, and some inequality techniques, sufficient...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2023/8226450 |
| _version_ | 1827089982343348224 |
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| author | Ruihong Liu Chuan Zhang Xianfu Zhang Fanwei Meng Hao Zhang |
| author_facet | Ruihong Liu Chuan Zhang Xianfu Zhang Fanwei Meng Hao Zhang |
| author_sort | Ruihong Liu |
| collection | DOAJ |
| description | This paper presents the stability analysis of a class of second-order linear partial differential equations (PDEs) on time scales with diffusion operator and first-order partial derivative. According to the time scale theory, the Lyapunov functional method, and some inequality techniques, sufficient conditions for exponential stability are strictly obtained, and the results are generalized for that where both the discrete-time and continuous-time cases are considered jointly. In addition, the theoretical results are applied to exponential synchronization of reaction-diffusion neural networks (RDNNs). Simulation examples are given to verify the feasibility of our results. |
| first_indexed | 2024-04-09T15:22:32Z |
| format | Article |
| id | doaj.art-63eee91f2dda4e79802c60cffe3f4041 |
| institution | Directory Open Access Journal |
| issn | 1607-887X |
| language | English |
| last_indexed | 2025-03-20T05:33:09Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj.art-63eee91f2dda4e79802c60cffe3f40412024-10-03T05:22:45ZengHindawi LimitedDiscrete Dynamics in Nature and Society1607-887X2023-01-01202310.1155/2023/8226450Stability Analysis of Second-Order Linear PDEs on Time ScalesRuihong Liu0Chuan Zhang1Xianfu Zhang2Fanwei Meng3Hao Zhang4School of Mathematical SciencesSchool of Mathematical SciencesSchool of Control Science and EngineeringSchool of Mathematical SciencesCollege of Information and ComputerThis paper presents the stability analysis of a class of second-order linear partial differential equations (PDEs) on time scales with diffusion operator and first-order partial derivative. According to the time scale theory, the Lyapunov functional method, and some inequality techniques, sufficient conditions for exponential stability are strictly obtained, and the results are generalized for that where both the discrete-time and continuous-time cases are considered jointly. In addition, the theoretical results are applied to exponential synchronization of reaction-diffusion neural networks (RDNNs). Simulation examples are given to verify the feasibility of our results.http://dx.doi.org/10.1155/2023/8226450 |
| spellingShingle | Ruihong Liu Chuan Zhang Xianfu Zhang Fanwei Meng Hao Zhang Stability Analysis of Second-Order Linear PDEs on Time Scales Discrete Dynamics in Nature and Society |
| title | Stability Analysis of Second-Order Linear PDEs on Time Scales |
| title_full | Stability Analysis of Second-Order Linear PDEs on Time Scales |
| title_fullStr | Stability Analysis of Second-Order Linear PDEs on Time Scales |
| title_full_unstemmed | Stability Analysis of Second-Order Linear PDEs on Time Scales |
| title_short | Stability Analysis of Second-Order Linear PDEs on Time Scales |
| title_sort | stability analysis of second order linear pdes on time scales |
| url | http://dx.doi.org/10.1155/2023/8226450 |
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