Dynamical Systems Seminar
主講者: 陳鞏 教授 (Texas A&M University)
講題: Taking the Poincare Section for the Wave Equation with Certain Types of Nonlinearities and Boundary Conditions in Multidimensional Settings to Prove Chaotic Oscillations
時間: 2014-01-08 (Wed.)  14:00 - 15:00
地點: 數學所 617 研討室 (台大院區)
Abstract: The proof of chaos for PDES with nonlinearities is considerably more challenging than the corresponding case for ODEs. It is especially so for dynamic nonlinear boundary value problems in multidimensional settings. In this talk, the speaker will introduce a novel way of averaging to prove chaos for the wave equation. The idea actually constitutes what can be interpreted as taking a Poincare section of the nonlinear equation, resulting in the reduction of dimensionality, from where chaos can be deduced. This approach presently only works for certain specific types of nonlinearities and boundary conditions but offers valuable insights for other more general equations and nonlinearities.
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