# Feedback stabilization and boundary controllability of the Korteweg-de Vries equation on a star-shaped network

## TL;DR

This paper studies the stabilization and boundary control of the Korteweg-de Vries equation on a star-shaped network, demonstrating energy decay and controllability results.

## Contribution

It introduces a model for the KdV equation on star-shaped networks, proving well-posedness, exponential energy decay, and boundary controllability.

## Key findings

- Energy of solutions decays exponentially over time.
- Established exact boundary controllability for the system.
- Proved well-posedness and regularity of the model.

## Abstract

We propose a model using the Korteweg-de Vries $(KdV)$ equation on a finite star-shaped network. We first prove the well-posedness of the system and give some regularity results. Then we prove that the energy of the solutions of the dissipative system decays exponentially to zero when the time tends to infinity. Lastly we show an exact boundary controllability result.