On the finite-time stabilization of strings connected by point mass

Abstract

In this paper, the problem of finite-time boundary stabilization of two strings connected by point mass is investigated. Based on the so-called Riemann invariant transformation, the vibrating strings are transformed in two hybridhyperbolic systems, and leads to the posedness of our system. In order to act in the system, it is desirable to choose boundary feedbacks, in this case, Hölderien stabilizing feedback laws to vanish in finite-time the right and the left of the solutions are considered.

Some results on the internal finite‐time stabilization of vibrating strings with interior mass

“…Hence, gathering together Equations (23) and 26, the inequality (21) holds for ≥ 3 4 , which proves that A is monotone. Part 2: Range condition.…”

“…As application, we have proved that waves produced by the motion of strings connected by point mass disappear in finite-time. In Belgacem et al, 23,24 the problem of boundary stabilization of (1)-(7) is reconsidered in finite-time. More precisely, boundary feedbacks that conduct to the dissipation of the system energy in finite-time are established.…”