| Project/Area Number |
13640200
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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 |
Basic analysis
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| Research Institution | Fukuoka University |
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Principal Investigator |
TANAKA Naoto (2003) Fukuoka University, Faculty of Science, Assistant Professor, 理学部, 助教授 (00247222)
山田 直記 (2001-2002) 福岡大学, 理学部, 教授 (50030789)
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| Co-Investigator(Kenkyū-buntansha) |
MARUO Kenji Kobe University, Faculty of Maritime Science, Professor, 海事科学部, 教授 (90028225)
KUROKIBA Masaki Fukuoka University, Faculty of Science, Assistant, 理学部, 助手 (60291837)
YAMADA Naoki Fukuoka University, Faculty of Science, Professor, 理学部, 教授 (50030789)
ISHII Katsuyuki Kobe University, Faculty of Maritime Science, Assistant Professor, 海事科学部, 助教授 (40232227)
田中 尚人 福岡大学, 理学部, 助教授 (00247222)
草野 尚 福岡大学, 理学部, 教授 (70033868)
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| Project Period (FY) |
2001 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | viscosity solution / subdifferential |
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| Research Abstract |
The aim of present research is to extend the notion of viscosity solutions to multi-valued nonlinear partial differential equations (PDE's) with subdifferential and to investigate the existence, uniqueness and other properties of solutions. The theory of viscosity solutions has been applied to wide class of frilly nonlinear PDE's. Among them, the obstacle problem is an important class of applications of viscosity solutions. We have put emphasis of the research on following three points:
1. We formulate various PDE's by subdifferential and apply the theory of viscosity solutions for it.
2. We compare the formulation by viscosity solution with known ones and study an advantage for it.
3. We prove solvability of various nonlinear PDE's and discuss the relation between the methods by viscosity solution.
It is shown that the notion of viscosity solutions are extended for nonlinear second order PDE's with subdifferential whose typical example is obstacle problem, and unique, existence theorem and stability of the solution are proved. Moreover, we investigate convergence of Yoshida approximation for subdiffrential term.
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