Boundary Feedback Stabilization of Two-Dimensional Shallow Water Equations with Viscosity Term

Autor:	Ben Mansour Dia, Oliver Dorn, Mouhamadou Samsidy Goudiaby
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	General Mathematics Computer Science (miscellaneous) shallow water flow Faedo–Galerkin method feedback control PDE’s stabilization Engineering (miscellaneous)
Zdroj:	Mathematics; Volume 10; Issue 21; Pages: 4036
ISSN:	2227-7390
DOI:	10.3390/math10214036
Popis:	This paper treats a water flow regularization problem by means of local boundary conditions for the two-dimensional viscous shallow water equations. Using an a-priori energy estimate of the perturbation state and the Faedo–Galerkin method, we build a stabilizing boundary feedback control law for the volumetric flow in a finite time that is prescribed by the solvability of the associated Cauchy problem. We iterate the same approach to build by cascade a stabilizing feedback control law for infinite time. Thanks to a positive arbitrary time-dependent stabilization function, the control law provides an exponential decay of the energy.
Databáze:	OpenAIRE
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