Development of study of nonlinear system as applied analysis

主要研究对象为动力学系统、非线性双曲守恒律和流体动力学方程。在考虑了模式的形成和解的结构之后，通过分析和计算机辅助分析，进一步研究了它们的解空间的全局结构，如分岔图和它们的稳定性。利用有限差分方法得到了Rayleigh-Benard热对流问题的整体分岔图，Benard-Marangoni热对流问题的分歧定理，以及对应于一类特殊的二自由度哈密顿量的Hamilton-Jacobi方程的一个构造性存在定理。

Main objects are Dynamical Systems, Nonlinear Hyperbolic Conservation Laws and Fluid Dynamical Equations. After considering the pattern formations and the structure of solutions we proceed to study their global structure of the solution spaces such as bifurcation diagrams and their stability by analysis and computer assisted analysis. Global bifurcation diagrams for Rayleigh-Benard heat convection problems, bifurcation theorems for Benard-Marangoni heat convection problems and a constructive existence theorem by a finite difference method for the Hamilton-Jacobi equation corresponding to a special Hamiltonian with two degree of freedom are obtained.