2006 Fiscal Year Final Research Report Summary
New development of convective reaction-diffusion systems and validation of numerical computation
| Project/Area Number |
16340042
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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 | 一般 |
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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, Faculty of Education, Professor, 教育学部, 教授 (00033887)
AIKI Toyohiko Gihu University, Faculty of Education, Associate Professor, 教育学部, 助教授 (90231745)
SHIBATA Yoshihiro Waseda University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (50114088)
SUZUKI Atsushi Kyusyu University, Department of Mathematical Sciences, Research Assistant, 大学院数理学研究院, 助手 (60284155)
MATSUMOTO Toshitaka Hiroshima University, Department of Mathematical and Life Sciences, Graduate School of Science, Research Assistant, 大学院理学研究科, 助手 (20229561)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Evolution operator / Convective reaction-diffusion system / Computational fluid dynamics / Nonlinear pertuebation of analytic semigroup / Multicomponent multiphase fluid phenomena / Mathematical modeling of nonlinear / Numerical simulation / Validation of numerical computation |
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| Research Abstract |
1. Researches on environmental fluids which are typical examples of multicomponent multiphase fluids. The continuous models have been obtained as coupled systems of Navier-Stokes systems and convective reaction-diffusion systems. Numerical models which are consistent with the continuous models were formulated as high precision, upwind and TVD schemes, and numerical simulations based on those models have been performed.
2. Fluid flow analysis around structures in environmental fluids. Numerical models for convective reaction-diffusion phenomena in environmental fluids have been developed. In particular, numerical analysis of air flows and motion of environmental pollutants in the over complex geographical topographies have been made.
3. Studies in time-dependent nonlinear perturbations of integrated semigroups. Time-dependent semilinear evolution equations are treated from the point of view of nonlinear evolution operator theory and have been applied to various mathematical models formulated as large-scale semilinear systems of partial differential equations.
4. The mathematical approach to HIV infection process and HAART therapies. Mathematical models of HIV disease progressions are formulated from the point of microbiology and physiology of HIV infection process in the immune system of an individual infected patient. The results of computer simulations based an the model agree with clinical data.
5. Researches on time-dependent nonlinear perturbations of analytic semigroups. A general theory for time-dependents nonlinear perturbation of analytic semigroups have been advanced and a characterization of the existence of nonlinear evolution operators has been obtained in terms of their semilinear generators. As a particular application of this theory, a bone remodeling model was completely solved.
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