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. || Close window ||