Work

Global approximate controllability of the Camassa–Holm equation by a finite dimensional force

Year: 2025

Type: article

Abstract: In this article, we consider the Camassa–Holm equation posed on the periodic domain T. We show that in any positive time, the Camassa–Holm equation is globally approximately controllable in Hs(T) for s > 3/2 by a three dimensional external force. The proof is based on Agrachev–Sarychev approach in geometric control theory. In particular, our three dimensional control prevents a finite time blow up of the solution of Camassa–Holm equation in Hs(T) for s > 3/2.

Source: Springer Link (Chiba Institute of Technology)

DOI: 10.1051/cocv/2025071/pdf

Authors: Shirshendu Chowdhury, Rajib Dutta, Debanjit Mondal

Institution: Indian Institute of Science Education and Research Kolkata

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Department of Science and Technology, Ministry of Science and Technology, India, Indian Institute of Science Education and Research Mohali, Indian Institute of Science Education and Research Kolkata

Awards: G5987201493, G6805594542, G7005538694