New Stability Criterion for the Dissipative Linear System and Analysis of Bresse System
In this article, we introduce a new approach to obtain the property of the dissipative structure for a system of differential equations. If the system has a viscosity or relaxation term which possesses symmetric property, Shizuta and Kawashima in 1985 introduced the suitable stability condition call...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/10/11/542 |
| _version_ | 1798042218498359296 |
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| author | Yoshihiro Ueda |
| author_facet | Yoshihiro Ueda |
| author_sort | Yoshihiro Ueda |
| collection | DOAJ |
| description | In this article, we introduce a new approach to obtain the property of the dissipative structure for a system of differential equations. If the system has a viscosity or relaxation term which possesses symmetric property, Shizuta and Kawashima in 1985 introduced the suitable stability condition called in this article Classical Stability Condition for the corresponding eigenvalue problem of the system, and derived the detailed relation between the coefficient matrices of the system and the eigenvalues. However, there are some complicated physical models which possess a non-symmetric viscosity or relaxation term and we cannot apply Classical Stability Condition to these models. Under this situation, our purpose in this article is to extend Classical Stability Condition for complicated models and to make the relation between the coefficient matrices and the corresponding eigenvalues clear. Furthermore, we shall explain the new dissipative structure through the several concrete examples. |
| first_indexed | 2024-04-11T22:32:26Z |
| format | Article |
| id | doaj.art-cc1ef7a58c05444585510464f4629d8e |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T22:32:26Z |
| publishDate | 2018-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-cc1ef7a58c05444585510464f4629d8e2022-12-22T03:59:21ZengMDPI AGSymmetry2073-89942018-10-01101154210.3390/sym10110542sym10110542New Stability Criterion for the Dissipative Linear System and Analysis of Bresse SystemYoshihiro Ueda0Faculty of Maritime Sciences, Kobe University, Kobe 658-0022, JapanIn this article, we introduce a new approach to obtain the property of the dissipative structure for a system of differential equations. If the system has a viscosity or relaxation term which possesses symmetric property, Shizuta and Kawashima in 1985 introduced the suitable stability condition called in this article Classical Stability Condition for the corresponding eigenvalue problem of the system, and derived the detailed relation between the coefficient matrices of the system and the eigenvalues. However, there are some complicated physical models which possess a non-symmetric viscosity or relaxation term and we cannot apply Classical Stability Condition to these models. Under this situation, our purpose in this article is to extend Classical Stability Condition for complicated models and to make the relation between the coefficient matrices and the corresponding eigenvalues clear. Furthermore, we shall explain the new dissipative structure through the several concrete examples.https://www.mdpi.com/2073-8994/10/11/542eigenvalue problemstability conditionstrict dissipativityregularity-loss structure |
| spellingShingle | Yoshihiro Ueda New Stability Criterion for the Dissipative Linear System and Analysis of Bresse System Symmetry eigenvalue problem stability condition strict dissipativity regularity-loss structure |
| title | New Stability Criterion for the Dissipative Linear System and Analysis of Bresse System |
| title_full | New Stability Criterion for the Dissipative Linear System and Analysis of Bresse System |
| title_fullStr | New Stability Criterion for the Dissipative Linear System and Analysis of Bresse System |
| title_full_unstemmed | New Stability Criterion for the Dissipative Linear System and Analysis of Bresse System |
| title_short | New Stability Criterion for the Dissipative Linear System and Analysis of Bresse System |
| title_sort | new stability criterion for the dissipative linear system and analysis of bresse system |
| topic | eigenvalue problem stability condition strict dissipativity regularity-loss structure |
| url | https://www.mdpi.com/2073-8994/10/11/542 |
| work_keys_str_mv | AT yoshihiroueda newstabilitycriterionforthedissipativelinearsystemandanalysisofbressesystem |