| Project/Area Number |
12554005
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 展開研究 |
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| Research Field |
Basic analysis
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| Research Institution | CHUO UNIVERSITY |
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Principal Investigator |
OHARU Shinnosuke Chuo University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (40063721)
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| Co-Investigator(Kenkyū-buntansha) |
KENMOCHI Nobuyuki Chiba University, Graduate School of Education, Professor, 教育学部, 教授 (00033887)
MIMURA Masayasu Hiroshima University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (50068128)
MATSUMOTO Toshitaka Hiroshima University, Graduate School of Science, Research Associate, 大学院・理学研究科, 助手 (20229561)
TAKAHASHI Tadayasu National Aerospace Laboratory of Japan, CFD Technology Center, Senior Researcher, CFD技術開発センター, 上級研究員
KOBAYASI Yoshikazu Niigata University, Faculty of Engineering, Professor, 工学部, 教授 (80092691)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Reactiondiffusion systems / Free boundary problems / Approximation solvability / Reliability analysis / Numerical simulation / Environmental fluids / Nonlinear evolution equations / Complex nonlinear phenomena |
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| Research Abstract |
In the research for the academic year of 2001, mathematical models describing various nonlinear advection-diffusion phenomena were intensively studied. A general theory of approximation-solvability for these problems has been extensively advanced from theoretical and numerical analytic points of view, and applications include mathematical approaches to various natural mechanisms, investigated through cooperation with experts from related fields. An intensive attempt has been made to advance a theory guaranteeing the approximation-solvability of these models. Reliability analysis of such computations has been made through numerical analytic studies.
1. A generation theory for locally Lipschitzian semigroups consistent with nonlinear evolution equations has been established in order to systematically investigate the solvability of various models describing nonlinear phenomena. New generation, characterization and approximation theorems have been obtained and applications made to mathemati
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cal models for interactions of nonlinear waves and cell proliferation.
2. New mathematical models describing ecosystems of microbes resident in coastal oceans have been constructed. Solvability has been investigated and numerical simulations performed. Numerical results were found to conform well with observational data.
3. Bone remodeling phenomena has been described by a new mathematical model and solvability and reliability of numerical simulations investigated. Numerical results were consistent with medical findings. It turns out that a new approach to mathematical formulation of biological phenomena has been exploited.
4. As an application of our methods to complex convection-diffusion phenomena in environmental fluids, flow analysis around vertical cylinders in sea water has been made and generation as well as interaction of vortices have been visualized on computers. Theoretical and reliability analysis for numerical simulations are now under investigation.
5. In order to treat two sex models involving birth, mortality, separation and migration rates, diffusion processes and marriage functions, a new theory of semilinear evolution equations has been developed, and again numerical results are consistent with statistical data. Less
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