Nonisotropic chaotic oscillations of the wave equation due to the interaction of mixing transport term and superlinear boundary condition

This paper studies the nonisotropic chaotic oscillations of the initial-boundary value problem of one-dimensional wave equation with a mixing transport term. It separately considers that the boundary condition at the right-end of the wave equation is a superlinear type and linear perturbation of such type, each causing the total energy of the underlying system to rise and fall due to the interaction with a mixing transport term. For each type of boundary condition, the occurrence of nonisotropic chaotic oscillations is rigorously proved. Numerical examples verify the effectiveness of theoretical prediction.