Boundary Control of Spherically Symmetric Oscillations of a~Three-Dimensional Ball

V. A. Il'in

Informatics and Automation, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 144-155

Résumé

The problem of boundary control of radially symmetric oscillations of a 3-ball that are described by a wave equation whose solutions $u(r, t)$ admit the existence of finite energy at every moment of time is studied. The state of an oscillating ball at every fixed moment of time $t$ is characterized by a pair of functions $\{ u (r, t), u_t (r, t) \}$. A minimal time interval $T$ is determined that is sufficient for changing an arbitrary initial state $\{ u (r, 0), u_t (r, 0) \}$ of the oscillation process to an arbitrary preset state $\{ u (r, T), u_t (r, T) \}$ with the use of a boundary control on the ball surface.