1996 Fiscal Year Final Research Report Summary
Nonlinear analysis and applications
| Project/Area Number |
08404003
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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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) |
FUJIMA Syouiti Hiroshima-U., Mathematics, Research associate, 理学部, 助手 (00209082)
TABATA Masahisa Hiroshima-U., Mathematics, Rrofessor, 理学部, 教授 (30093272)
SAKAMOTO Kunimochi Hiroshima-U., Mathematics, Assist. Peofessor, 理学部, 助教授 (40243547)
TAIRA Kazuaki Hiroshima-U., Mathematics, Rrofessor, 理学部, 教授 (90016163)
MATSUMOTO Toshitaka Hiroshima-U., Mathematics, Research associate, 理学部, 助手 (20229561)
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| Project Period (FY) |
1996
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| Keywords | nonlinear analysis / evolution equations / numerical method / computational methods / infinite dimensinoal dynamical system / nonlinear elliptic equation / reaction-diffusion system / nonlinear conveetive diffusion equation |
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| Research Abstract |
In this research project nonlinear problems arising in a variety of mathematical models have been treated in terms of evolution equation, infinite dimensional dynamical system, pde, and unmerical analysis. By means of the new knowledge and methods invented through this research, significant nonlinear theories were advaced. Extensive studies of important nonlinear problem have been mede from the theoretical pont of view and that of application.
1.Fundamental results on time-dependent nonlinear perturbations of integrated semigroups were obtained. These results can be applied to various mathemtical models in a systematic way.
2.A generation theory for evolution operators was extended so that a broad class of nonlinear degenerate parabolic equations may be treated in the framework.
3.Nonlinear problems related to nonlinear elastostaics, chemical kinetics and differential geometry were systimatically studied in terms of nonlinear elliptic problem.
4.Formation of space-time patterns of the solu
… More
tions of a class of semilinear evolution systems exothermic reaction-difusion processes was investigated inn detail.
5.New numerical methods for the analysis of fluid dynamics were developed and applied to incompressible fluid flow. Theoretical studies of the methods and algorithms were made. Also, convergence of approximate solutions and the accuracy were investigated.
Nonlinear analysis is incorported with the studies in nonlinear problems arising in the current science and technology. The theories and applications are closely linked and advanced in an interdisciplinary way. In order to accomplish this comprehensive study, effective research communication as well as exchange of technical knowledge is particularly important. During to the geant-in-aid, most of the aimed results were obtained. In particular, an international conference on evolution equations and their applications to technology was held with the participation of leading researchers in the related fields and this support is gretly appreciated. Less
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