数学一级学科Seminar 770
主题：偏微分方程的局部对称及相联系的问题
报告人：Bluman 教授（加拿大英属哥伦比亚大学)
时间：2013年10月10日（周四)14:00
地点：校本部F307
主办部门：理学院数学系

摘要: A PDE system is a compact way of describing a family of surfaces (solutions of the PDE system). A symmetry of a PDE system transforms each solution to another solution of the system. Of particular interest are contiuous symmetries that are essentially deformations of the solution manifold. From this topological point of view, it follows that every nontrivial PDE system has continuous symmetries..
Much work of the past 25 years focusses on how to systematically find and use nonlocal symmetries for a given PDE system. It will be seen that the starting point to seek nonlocal symmetries is to find systematically nonlocally related systems for a given PDE system. It will be shown that any conservation law or any point symmetry of a given PDE system naturally and systematically yields a nonlocally related system which in turn may yield nonlocal symmetries for the given PDE system. The special problems that arise for multidimensional PDEs will be considered. Numerous examples will be exhibited.P