Abstract
Spatiotemporal chaos or turbulence in partial differential equations is a vastly open research field. In this paper, we show that imbalance of boundary energy flow due to certain types of nonlinear feedback boundary control can cause chaotic vibration of the one- dimensional wave equation. We first show that if there is a linear amplifier with feedback gain T) at the left end point, and if there is cubic velocity feedback damping at the right end point, then spatiotemporal chaos of the gradient (Wx,Wt) will occur as the gain parameter n is tuned. We then show through numerical simulations of concrete examples what may happen if a more general polynomial feedback is applied at the right end point. Chaotic profiles of wave motion are illustrated by computer graphics.