The control of string in two interior points (Q1183087)

The author considers the equation of the motion of a string with fixed endpoints. The string is initially at rest: two independent controls are applied impulsionally at two interior points. Let \(R(t)\) be the set of reachable states in \(L^ 2\). Then, there is a critical value \(T_ 0\) such that \(R(t)\) is increasing for \(t\in[0,T_ 0]\) and \(R(t)=R(T_ 0)\) for \(t>T_ 0\). The aim of the paper is to compute this critical value \(T_ 0\).