1995 Fiscal Year Final Research Report Summary
Evolution equations and their applications to nonlinear problems
| Project/Area Number |
06452011
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | HIROSHIMA UNIVERSITY |
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Principal Investigator |
OHARU Shinnosuke Hiroshima-U., Mathematics, Professor, 理学部, 教授 (40063721)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAMOTO Kunimochi Hiroshima-U., Mathematics, Lecturer, 理学部, 講師 (40243547)
OKAMOTO Kiyosato Hiroshima-U., Mathematics, Professor, 理学部, 教授 (60028115)
KUBO Izumi Hiroshima-U., Mathematics, Professor, 理学部, 教授 (70022621)
MAEDA Fumiyuki Hiroshima-U., Mathematics, Professor, 理学部, 教授 (10033804)
MATSUMOTO Toshitaka Hiroshima-U., Mathematics, Research associate, 理学部, 助手 (20229561)
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| Project Period (FY) |
1994 – 1995
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| Keywords | Nonlinear evolution system / Evolution operator / Nonlinear semigroup / Nonlinear perturbation / Quasilinear elliptic equation / Dynamical system / Stochastic analysis / Feynman path integral |
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| 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 convection-diffusion 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 reaction-diffusion systems.
3. Global and boundary behaivior of the solutions of quasilinear ellipti
… More
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 reaction-diffusion, phase transition, hysteresis, motion of viscoelastic bodies with memory and convection-diffusion 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 grant-in-aid, satisfactory results were obtained and this support is graeatly appreciated. These results will be published in the forms of research papers or books. Less
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