Control and stabilization of PDE on networks


Speciality : Mathématiques Appliquées

5/07/2023 - 15:00 Hugo Parada (Université Grenoble Alpes) Amphithéâtre Maison du doctorat Jean Kuntzmann (premier étage) 110 rue de la Chimie 38400 Saint-Martin-d'Hères

Keywords :
  • stabilisation
  • feedback retardés
  • équations aux dérivées partielles
  • saturation
In this thesis, we study stabilization problems for the Korteweg-de Vries (KdV) equation in a bounded domain and on a star-shaped network structure. More specifically, the focus of this thesis is to analyze the cases where the feedback terms include delay and saturation. In Chapter 3, we deal with the internal stabilization of the nonlinear KdV equation posed on a star-shaped network when the feedback terms involve time delay. Using Lyapunov techniques and an appropriated observability inequality, we managed to show the exponential stability of the associated system. In Chapter 4, we study the saturated internal stabilization of the KdV equation on a star-shaped network. In this case, we show first a global well-posedness result by using an appropriated linear system and the Kato smoothing property. Then, we show the exponential stability via a contradiction argument and an observability inequality. In Chapter 5, the stability analysis of the KdV equation on a bounded domain in presence of boundary saturation is studied. Using nonlinear semigroup theory and fixed-point arguments, we show the well-posedness. The exponential stability is proved by using compactness ideas to get an observability inequality. In Chapter 6, we consider the stability analysis of the KdV equation on a bounded domain with time-dependent delay on the boundary or internal feedbacks. We study the well-posedness using time-varying semigroup theory. The exponential stability is derived by using Lyapunov theory. Finally, in Chapter 7 some comments and future research problems are addressed.


  • HDR, MCF Emmanuelle Crépeau (Laboratoire Jean Kuntzmann, Université Grenoble Alpes )
  • HDR, DR1 Christophe Prieur (Gipsa-Lab, Université Grenoble Alpes )


  • Professor Bing-Yu Zhang (University of Cincinnati )
  • Professeur Franck Boyer (Université Toulouse III - Paul Sabatier )


  • Professeur Hoai-Minh Nguyen (Sorbonne Université )
  • HDR, MCF Julie Valein (Université de Lorraine )
  • Professeur Emmanuel Witrant (Université Grenoble Alpes )
  • Professor Eduardo Cerpa (Pontificia Universidad Católica de Chile )