In this talk, we consider the one (and two)-dimensional wave equation on the unit interval [0, 1]. At the left end x = 0, an energy injecting boundary condition is posed, and at the right end, x = 1, the boundary condition is a cubic nonlinearity, which is a van der Pol type condition. This nonlinear boundary condition behaves like a van der Pol oscillator, causing the total energy to rise and fall within certain bounds regularly or irregularly. Theoretical and numerical analysis are presented.
冯兆生,美国德克萨斯大学讲席教授、Distinguished Career Award 获得者。主要研究方向是非线性分析,动力系统,数学物理问题,数值分析模拟等,现任国际知名学术期刊CNSNS的共同主编,同时担任多个国际SCI学术期刊的编委和AIMS应用数学系列数学丛书的编委。