Two approaches for the stabilization of nonlinear KdV equation with boundary time-delay feedback
Year: 2017
Type: preprint
Abstract: This article concerns the nonlinear Korteweg-de Vries equation with boundary time-delay feedback. Under appropriate assumption on the coefficients of the feedbacks (delayed or not), we first prove that this nonlinear infinite dimensional system is well-posed for small initial data. The main results of our study are two theorems stating the exponential stability of the nonlinear time delay system. Two different methods are employed: a Lyapunov functional approach (allowing to have an estimation on the decay rate, but with a restrictive assumption on the length of the spatial domain of the KdV equation) and an observability inequality approach, with a contradiction argument (for any non critical lengths but without estimation on the decay rate). Some numerical simulations are given to illustrate the results.
Source: arXiv (Cornell University)
Institutions: Centre National de la Recherche Scientifique, Université Toulouse III - Paul Sabatier, Laboratoire d'Analyse et d'Architecture des Systèmes, Université de Toulouse, Laboratoire Magmas et Volcans, Institut national de recherche en sciences et technologies du numérique, Institut Élie Cartan de Lorraine, SPHINX: Heterogeneous Systems: Inverse Problems, Control and Stabilization, Simulation, Université de Lorraine
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W2953340982