Boundary controllability of the Korteweg-de Vries equation on a tree-shaped network

Eduardo Cerpa (1) , Emmanuelle Crépeau (2) , Julie Valein (3, 4)

1 Departamento de Matematica, Universidad Tecnica Federico Santa Maria
2 EDP - Equations aux Dérivées Partielles
3 IECL - Institut Élie Cartan de Lorraine
4 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization

Controllability of coupled systems is a complex issue depending on the coupling conditions and the equations themselves. Roughly speaking, the main challenge is controlling a system with less inputs than equations. In this paper this is successfully done for a system of Korteweg-de Vries equations posed on an oriented tree shaped network. The couplings and the controls appear only on boundary conditions.

Domaines: Optimisation et contrôle [math.OC]

Eduardo Cerpa, Emmanuelle Crépeau, Julie Valein. Boundary controllability of the Korteweg-de Vries equation on a tree-shaped network. 2019. ⟨hal-02137907v1⟩