Lyapunov Exponential Stability of the Shallow Water Equations in Trapezoidal Channel
This paper solves the problem of the exponential stability in L2-norm of Saint-Venant equations linear hyperbolic system for a non-prismatic and non-rectangular channel. We consider the general case of systems containing not only both arbitrary friction and spatially varying slopes but also spatiall...
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| Format: | Article |
| Language: | English |
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Mathyze Publishers
2024-04-01
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| Series: | Pan-American Journal of Mathematics |
| Online Access: | https://mathyze.com/index.php/pajm/article/view/175 |
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| author | Seydou Sore Babacar Mbaye Ndiaye Yacouba Simpore |
| author_facet | Seydou Sore Babacar Mbaye Ndiaye Yacouba Simpore |
| author_sort | Seydou Sore |
| collection | DOAJ |
| description | This paper solves the problem of the exponential stability in L2-norm of Saint-Venant equations linear hyperbolic system for a non-prismatic and non-rectangular channel. We consider the general case of systems containing not only both arbitrary friction and spatially varying slopes but also spatially varying channel dimensions (width and lateral slope), leading to non-uniform stationary states. An explicit quadratic Lyapunov function is constructed as a weighting function for steady-state small perturbations. We then show that local exponential stability of Saint-Venant equations linear system for a trapezoidal channel can be guaranteed in the L2-norm by an appropriate choice of boundary feedback control. Finally, we give explicitly that control. |
| format | Article |
| id | doaj-art-ac6dde4f79484d6685249a0e22c915c4 |
| institution | OA Journals |
| issn | 2832-4293 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Mathyze Publishers |
| record_format | Article |
| series | Pan-American Journal of Mathematics |
| spelling | doaj-art-ac6dde4f79484d6685249a0e22c915c42025-08-20T02:34:59ZengMathyze PublishersPan-American Journal of Mathematics2832-42932024-04-013010.28919/cpr-pajm/3-946Lyapunov Exponential Stability of the Shallow Water Equations in Trapezoidal ChannelSeydou Sore0Babacar Mbaye NdiayeYacouba SimporeUniversité Norbert ZONGOThis paper solves the problem of the exponential stability in L2-norm of Saint-Venant equations linear hyperbolic system for a non-prismatic and non-rectangular channel. We consider the general case of systems containing not only both arbitrary friction and spatially varying slopes but also spatially varying channel dimensions (width and lateral slope), leading to non-uniform stationary states. An explicit quadratic Lyapunov function is constructed as a weighting function for steady-state small perturbations. We then show that local exponential stability of Saint-Venant equations linear system for a trapezoidal channel can be guaranteed in the L2-norm by an appropriate choice of boundary feedback control. Finally, we give explicitly that control.https://mathyze.com/index.php/pajm/article/view/175 |
| spellingShingle | Seydou Sore Babacar Mbaye Ndiaye Yacouba Simpore Lyapunov Exponential Stability of the Shallow Water Equations in Trapezoidal Channel Pan-American Journal of Mathematics |
| title | Lyapunov Exponential Stability of the Shallow Water Equations in Trapezoidal Channel |
| title_full | Lyapunov Exponential Stability of the Shallow Water Equations in Trapezoidal Channel |
| title_fullStr | Lyapunov Exponential Stability of the Shallow Water Equations in Trapezoidal Channel |
| title_full_unstemmed | Lyapunov Exponential Stability of the Shallow Water Equations in Trapezoidal Channel |
| title_short | Lyapunov Exponential Stability of the Shallow Water Equations in Trapezoidal Channel |
| title_sort | lyapunov exponential stability of the shallow water equations in trapezoidal channel |
| url | https://mathyze.com/index.php/pajm/article/view/175 |
| work_keys_str_mv | AT seydousore lyapunovexponentialstabilityoftheshallowwaterequationsintrapezoidalchannel AT babacarmbayendiaye lyapunovexponentialstabilityoftheshallowwaterequationsintrapezoidalchannel AT yacoubasimpore lyapunovexponentialstabilityoftheshallowwaterequationsintrapezoidalchannel |