Project/Area Number  06640181 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
Geometry

Research Institution  Ryukoku University 
Principal Investigator 
ITO Toshikazu Faculty of Economy, Ryukoku University, Professor, 経済学部, 教授 (60110178)

CoInvestigator(Kenkyūbuntansha) 
MORITA Yoshihisa Faculty of Science & Technology, Ryukoku Univ., Assosiate Professor, 理工学部, 助教授 (10192783)
OKA Hiroe Faculty of Science & Technology, Ryukoku Univ., Associate Professor, 理工学部, 助教授 (20215221)
YOTSUTANI Shoji Faculty of Science & Technology, Ryukoku Univ., Professor, 理工学部, 教授 (60128361)
MATSUMOTO Waichiro Faculty of Science & Technology, Ryukoku Univ., Professor, 理工学部, 教授 (40093314)

Project Fiscal Year 
1994 – 1995

Project Status 
Completed(Fiscal Year 1995)

Budget Amount *help 
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1995 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1994 : ¥900,000 (Direct Cost : ¥900,000)

Keywords  singular points of holomorphic vector fields / strongly hyperbolic system / reaction diffusion system / asymptotic stability / dissipative dynamical system / inertial manifold / Lorenz attractors / piecewise linear vector fields / 正則ベクトル場の特異点 / 強双曲型偏微分方程式系 / 反応拡散方程式 / 漸近安定性 / 散逸力学系 / 慣性多様体 / ローレンツ型アトラクター / 区分線型ベクトル場 / 正則ベクトル場 / ザイフェルト予想 / 偏微分方程式 / 擬微分作用素のシンボル / 半線形楕円型方程式 / 半線形放物型方程式 / ベクトル場の退化特異点 / ローレンツアトラクター 
Research Abstract 
T.Ito counted the number of compact leaves of one dimensional nonsingular foliation on the 2n1 dimensional sphere S^<2n1> associated with holomorphic vector fields, using PoincareDulac polynomialization Theorem at isolated singular point. W.Matsumoto has studied the characterization of the strongly hyperbolic systems of partial differential equations. He showed that in case where the coefficients depend only on the time variable, the strongly hyperbolic systems can be transformed to a Fuchsian with diagonal principal part at each point of the fiber space. This condition is the necessary and sufficient for the strong hyperbolicity when the dimension of xspace is one. On the other hand, in higher dimension case, he proposed a conjecture that the uniformity on the dual variables of transforming matrix might be necessary, and he showed that Petrovski's nonstrongly hyperbolic system is unstable and easily change to a strongly hyperbolic system by a small perturbation. S.Yotsutani has st
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udied the asymptotic behavior and the rate of the convergence of solutions to a practical mathematical model of an chemical interfacial reaction, which is a parabolic system with nonlinear bondary conditions. Moreover, he has also studied some class of semilinear elliptic equations, and obtained a strong classification theorem of structure of positive radial solutions. The theorem claims that structure of solution is closely related with zeros of a function determined by coefficients and power of a nonlinear term. H.Oka showed that chaotic attractor of Lorenztype is generated locally by an unfolding of some degenerate singularity. Also, she studied some piecewise linear vector fields and found a bifurcation including infinitely many doubling of codimension 2 homoclinic orbits which is called orbitflip type. Y.Morita obtained with H.Ninomiya and E.Yanagida a theorem on the existence of an inertial manifold for a reactiondiffusion equation with nonlinear boundary condition. Moreover they gave the reduced finitedimensional equation on the manifold together with applications to specific equations. Here the inertial manifold means a finitedimensional invariant manifold which attracts every orbit in a phase space. Y.Morita studied in a joint work with K.Mischaikow a global structure of the dissipative dynamical system for the GinzburgLandau equation in a bounded interval and they showed a Morese structure of the dynamics. Y.Morita with S.Jimbo obtained an instability theorem of nonconstant equilibrium solutions to the GinzburgLandau equation in any convex domain while they constructed stable nonconstant solutions in an annulus domain. Less
