1998 Fiscal Year Final Research Report Summary
Mathematical Research of Nonlinear Phenomena with Phase Transitions
| Project/Area Number |
09640154
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Chiba University |
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Principal Investigator |
KENMOCHI Nobuyuki Chiba Univ., Fac.Education, Professor, 教育学部, 教授 (00033887)
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| Co-Investigator(Kenkyū-buntansha) |
ITO Akio Gifu Univ., Fac.Engineering, Assistant, 工学部, 助手 (30303506)
AIKI Toyohiko Gifu Univ., Fac.Education, Ass.Prof., 教育学部, 助教授 (90231745)
KOSHIGOE Hideyuli Chiba Univ., Fac.Engineering, Ass.Prof., 工学部, 助教授 (70110294)
UZAWA Masakatsu Chiba Univ., Fac.Education, Professor, 教育学部, 教授 (80009026)
KURANO Masami Chiba Univ., Fac.Education, Professor, 教育学部, 教授 (70029487)
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| Project Period (FY) |
1997 – 1998
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| Keywords | phase transition / subdifferential / evolution equation / Stefan Problem / free boundary / convex function / obstacle problem / variational inequality |
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| Research Abstract |
The main objective of this project is to treat various nonlinear phenomena with phase transitions from interdisciplinary points of view. Our research is concerned with their modellings and theoretical analysis by using tools in nonlinear functional analysis for instance the subdifferential operaors theory of convex functions.
During the term of this project we found that many solid-liquid or solid-solid phase transition models are able to be handled within the perturbation theory of nonlinear evolution equations generated by subdifferentials in Hilbert spaces. Moreover, we pro- posed a class big enough of dynamical processes, including nonlinear phenomena in our consideration as typical examples, and evolved the stability theory for it ; in fact, we suc- ceeded in the construction of global attractors. In our set-up, one of the most important characteristics is that the domain of dynamical process depends upon time.
Also, as co-products of our results obtained in this project, an important question, which had been remained open for 30 years, about nonlinear elliptic operators was solved. This is a big contribution in this field, too.
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