Abstract:
The question is studied of the existence of a minimal time interval $T_0$ and a boundary control at one endpoint $x=0$ or boundary controls at the two endpoints $x=0$ and $x=l$ which during the time $T_0$ transform the process described by the equation $k(x)[k(x)u_x(x,t)]_x-u_{tt}(x,t)=0$ (and, in particular, by the wave equation in the case $k(x)=1$), or the process described by the telegraph equation $u_{tt}(x,t)-u_{xx}(x,t)+C^2u(x,t)=0$, from an arbitrarily given initial state $\{u(x,t)=\phi(x),u_t(x,t)=\psi(x)\}$ to an arbitrarily given final state $\{u(x,T)=\phi_1(x)$, $u_t(x,T)=\psi_1(x)\}$.
All the desired boundary controls are produced in explicit analytic form.
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