Analysis Seminar
主講者: | 1.曾根良夫教授(京都大學&中研院) 2.曾我幸平博士(早稻田大學) |
講題: | 1.Kinetic Theory and Gas Dynamics 2.Periodic Solutions of the Forced Burgers Equation and Hamiltonian Systems |
時間: | 2008-11-03 (Mon.) 10:00 - 13:00 |
地點: | |
Abstract: | 2.We consider the forced Burgers equation, where the forcing term is Z^2-periodic. Our problem is to find $Z^2$-periodic (weak) solutions of the equation in a constructive way. First, I talk about the connection between the forced Burgers equation and Hamiltonian systems: One of the central issues in the theory of Hamiltonian systems is to look for their invariant manifolds. The graph of Z^2-periodic solution to the forced Burgers equation plays an important role in the issue. Second, I show convergence proofs and numerical simulations to two methods of constructing Z^2-periodic solutions: The one is based on the long time behavior of Lax-Friedrichs difference scheme. The other is based on the Newton’s methods, regarding Z^2-periodic solutions as fixed points of the Poincare map. |
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