Growth rates of total variations of snapshots of 1D linear wave equations with nonlinear right-end boundary conditions

This paper is concerned with the one-dimensional wave equation on a unit interval, where the left-end boundary condition (BC) is linear, while the right-end BC is general nonlinearity. We give the dynamical behavior of the Riemann invariants ( u , v ) of the wave equation in terms of the total variations, and show that chaotic vibration occurs when η enters a certain parameter range.