Development of study of nonlinear system as applied analysis

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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.