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.