Nonisotropic chaotic vibrations of a 2D hyperbolic PDE.

Abstract

Little seems to be known about the chaos of the two-dimensional (2D) hyperbolic partial differential equations (PDEs). The objective of this paper is to study the nonisotropic chaotic vibrations of a system governed by a 2D linear hyperbolic PDE with mixed derivative terms (MDTs) and a nonlinear boundary condition (NBC), where the interaction between MDTs and NBC causes the energy of such a system to rise and fall. The 2D hyperbolic system is proved to be topologically conjugate with the corresponding Riemann invariants, which are rigorously proved to be chaotic. Two numerical examples are carried out to demonstrate the theoretical results.