CHAOTIC VIBRATIONS OF THE ONE-DIMENSIONAL MIXED WAVE SYSTEM

Abstract

In this paper, we consider the initial-boundary value problem of the one-dimensional linear mixed wave equation omega(tt) - d omega(tx) - c(2)omega(xx) = 0 (d is an element of R, c > 0) on an interval, where the boundary condition at the left endpoint is linear, pumping energy into the system, while the boundary condition at the right endpoint has odd-degree nonlinearity. This problem is said to be the one-dimensional mixed wave system. The solution of the one-dimensional mixed wave system corresponds to the iteration of an interval map h. Thus, the mixed wave system is said to be chaotic if the interval map h is chaotic in the sense of Li-Yorke. In this paper, we show that the mixed wave system is chaotic under some conditions.