Project/Area Number  06452011 
Research Category 
GrantinAid for Scientific Research (B).

Research Field 
解析学

Research Institution  HIROSHIMA UNIVERSITY 
Principal Investigator 
OHARU Shinnosuke HiroshimaU., Mathematics, Professor, 理学部, 教授 (40063721)

CoInvestigator(Kenkyūbuntansha) 
MATSUMOTO Toshitaka HiroshimaU., Mathematics, Research associate, 理学部, 助手 (20229561)
SAKAMOTO Kunimochi HiroshimaU., Mathematics, Lecturer, 理学部, 講師 (40243547)
内藤 学 広島大学, 理学部, 助教授 (00106791)
OKAMOTO Kiyosato HiroshimaU., Mathematics, Professor, 理学部, 教授 (60028115)
MAEDA Fumiyuki HiroshimaU., Mathematics, Professor, 理学部, 教授 (10033804)
KUBO Izumi HiroshimaU., Mathematics, Professor, 理学部, 教授 (70022621)

Project Fiscal Year 
1994 – 1995

Project Status 
Completed(Fiscal Year 1995)

Budget Amount *help 
¥5,800,000 (Direct Cost : ¥5,800,000)
Fiscal Year 1995 : ¥2,700,000 (Direct Cost : ¥2,700,000)
Fiscal Year 1994 : ¥3,100,000 (Direct Cost : ¥3,100,000)

Keywords  Nonlinear evolution system / Evolution operator / Nonlinear semigroup / Nonlinear perturbation / Quasilinear elliptic equation / Dynamical system / Stochastic analysis / Feynman path integral / 非線形発展系 / 発展作用素 / 非線形半群 / 非線形摂動 / 準線形楕円型方程式 / 力学系 / 反応拡散系 / ファイマン経路積分 / 発展方程式 / 半線形楕円型方程式 / 移流・拡散方程式 / 振動解 
Research Abstract 
In this research project a variety of nonlinear problems entailing partial defferential equations have been treated from the point of view of the theory of evolution equations. With the aid of the newest knowledge and methods invented in the related fields, useful nonlinear theories were advanced and their applications, numerical analytic approaches and numerical experiments were extensively investigated. 1. General classes of nonlinear semigroups and evolution operators were introduced and the associated generation and approximation theories were obtained. These results were applied to typical evolution systems such as nonlinear convectiondiffusion equations, conservation laws and nonlinear dispersive systems. 2. Optimal results for nonlinear perturbations of analytic semigroups were obtained and applied to nonlinear models which arised in physiology, population dynamics and the study of reactiondiffusion systems. 3. Global and boundary behaivior of the solutions of quasilinear ellipti
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c and parabolic equations was investigated in detail from the point of view of potential theory. 4. A new path integral approach to evolution systems appearing in mathematical physics was formulated. 5. Various natural phenomena such as reactiondiffusion, phase transition, hysteresis, motion of viscoelastic bodies with memory and convectiondiffusion phenomena were extensively studied from the points of view of the theories of evolution equations, dynamical systems and stochastic analysis and numbers of new interesting results were obtained. The study of evolution equations is incorporated in various sound ways with the studies in important nonlinear evolution problems that had arised in scientific fields. In order to accomplish this comprehensive study, swift and effective research communication as well as exchange of technical knowledge is essential. Owing to this grantinaid, satisfactory results were obtained and this support is graeatly appreciated. These results will be published in the forms of research papers or books. Less
