Boundary feedback stabilization of quasilinear hyperbolic systems with zero characteristic speed
In this paper, we investigate the boundary feedback stabilization of a quasilinear hyperbolic system with zero characteristic speed and a partially dissipative structure. This structure enables us to construct a Lyapunov function that guarantees exponential stability for the H2 solution. We also in...
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| Format: | Article |
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Vilnius Gediminas Technical University
2025-04-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://bme.vgtu.lt/index.php/MMA/article/view/20890 |
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| _version_ | 1849712686639611904 |
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| author | Zhiqiang Wang Wancong Yao |
| author_facet | Zhiqiang Wang Wancong Yao |
| author_sort | Zhiqiang Wang |
| collection | DOAJ |
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In this paper, we investigate the boundary feedback stabilization of a quasilinear hyperbolic system with zero characteristic speed and a partially dissipative structure. This structure enables us to construct a Lyapunov function that guarantees exponential stability for the H2 solution. We also introduce another set of stability conditions by restricting terms corresponding to zero eigenvalues to the dissipative part, which still ensures exponential stability. As an application, we achieve feedback stabilization for the modified model of neurofilament transport in axons.
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| format | Article |
| id | doaj-art-043c79de2c0b4e7aac685f20ac7691b7 |
| institution | DOAJ |
| issn | 1392-6292 1648-3510 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj-art-043c79de2c0b4e7aac685f20ac7691b72025-08-20T03:14:12ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102025-04-0130210.3846/mma.2025.20890Boundary feedback stabilization of quasilinear hyperbolic systems with zero characteristic speedZhiqiang Wang0Wancong Yao1School of Mathematical Sciences, Fudan University, 200433 Shanghai, China; School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, 200433 Shanghai, ChinaSchool of Mathematical Sciences, Fudan University, 200433 Shanghai, China; Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China In this paper, we investigate the boundary feedback stabilization of a quasilinear hyperbolic system with zero characteristic speed and a partially dissipative structure. This structure enables us to construct a Lyapunov function that guarantees exponential stability for the H2 solution. We also introduce another set of stability conditions by restricting terms corresponding to zero eigenvalues to the dissipative part, which still ensures exponential stability. As an application, we achieve feedback stabilization for the modified model of neurofilament transport in axons. https://bme.vgtu.lt/index.php/MMA/article/view/20890quasilinear hyperbolic systemzero characteristic speedfeedback stabilizationLyapunov function |
| spellingShingle | Zhiqiang Wang Wancong Yao Boundary feedback stabilization of quasilinear hyperbolic systems with zero characteristic speed Mathematical Modelling and Analysis quasilinear hyperbolic system zero characteristic speed feedback stabilization Lyapunov function |
| title | Boundary feedback stabilization of quasilinear hyperbolic systems with zero characteristic speed |
| title_full | Boundary feedback stabilization of quasilinear hyperbolic systems with zero characteristic speed |
| title_fullStr | Boundary feedback stabilization of quasilinear hyperbolic systems with zero characteristic speed |
| title_full_unstemmed | Boundary feedback stabilization of quasilinear hyperbolic systems with zero characteristic speed |
| title_short | Boundary feedback stabilization of quasilinear hyperbolic systems with zero characteristic speed |
| title_sort | boundary feedback stabilization of quasilinear hyperbolic systems with zero characteristic speed |
| topic | quasilinear hyperbolic system zero characteristic speed feedback stabilization Lyapunov function |
| url | https://bme.vgtu.lt/index.php/MMA/article/view/20890 |
| work_keys_str_mv | AT zhiqiangwang boundaryfeedbackstabilizationofquasilinearhyperbolicsystemswithzerocharacteristicspeed AT wancongyao boundaryfeedbackstabilizationofquasilinearhyperbolicsystemswithzerocharacteristicspeed |