Analysis and Computation of Nonlinear Structures

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For the purpose of solving the structure of nonlinear phenomena and their dynamics, the present research project has been dealt with the following five major fields : (1) Nonlinear structure in fluid dynamics, (2) Dynamics of free boundaries, (3) Scientific computing of fracture phenomena, (4) Singular points appearing in differential equations, (5) Tracking of bifurcation structure.Important results are as follows. Air flow computation around an automated guided vehicle (Tabata), Finite element analysis of axisymmetric flow problems (Tabata), Bifurcation of progressive waves of finite depth (Okamoto), Vortex sheet roll-up in the background shear flow (Okamoto) and Flow problems with unilateral boundary conditions (Fujita). Pattern selections for two breathers (Ikeda and Nishiura), Global bifurcation diagram of traveling pulses (Ikeda), Existence and stability of interfacial patterns in higher dimensional spaces (Nishiura), Singular limit systems derived from reaction-diffusion systems … More (Mimura), Numerical computation of generalized curve shortening equations (Tsutsumi) and Free boundaries in porous media (Kawarada) in (2). The arbitrary line method for elasto-plastic problems (Miyoshi) and Improved 4-node quadrilateral plate bending element (Kikuchi) in (3). Blow-up problems of degenerate parabolic equations (Tsutsumi and Matano) in (4). Reaction-diffusion systems and inertial manifolds (Morita) and Navier-Stokes flows down an inclined plate (Nishida) in (5). Other related topics have been also studied, Brain dynamics (Fujii) and Application of chaos theory to social sciences (Yamaguti) for instance.The present project is characterized by the mathematical analysis in cooperation with numerical computation. The following results have been obtained in the field of the development of numerical methods : An improved conjugate gradient method for large systems of linear equations (Mitsui), Quadrature formulas for Fourier type integrals obtained by variable transformation (Mori), Computer aided proofs for bifurcation problems in equations of fluid dynamics (Nishida) and The domain dependence of convergence rate of a domain decomposition method (Fujita) for instance. Less