1996 Fiscal Year Final Research Report Summary
Viscosity solutions of nonlinear partial differential equations and its applications
| Project/Area Number |
06640255
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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 | Miyazaki University |
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Principal Investigator |
YAMADA Naoki Faculty of Engeneering, Professor, 工学部, 教授 (50030789)
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| Co-Investigator(Kenkyū-buntansha) |
OGATA Akio Faculty of Education, Professor, 教育学部, 教授 (80040921)
KAWANO Nichiro Faculty of Education, Professor, 教育学部, 教授 (20040983)
SENBA Takasi Faculty of Engeneering Associate Professor, 工学部, 助教授 (30196985)
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| Project Period (FY) |
1994 – 1996
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| Keywords | viscosity solutions / Keller-Segel system / semilinear elliptic equations |
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| Research Abstract |
1. We established existence and uniqueness results of viscosity solutions for nonlinear partial differential equations involving nonlocal terms. such nonlocal terms arise in the Hamilton-Jacobi-Bellman equations associated with the dymnamical systems with jumps.
2. We investigated the blow-up property or time global existence of the solutions for Keller-Segel systems. These systems are mathematical models of chemotaxis.
3. We obtained existence results of radially symmetric nodal solutions for semilinear elliptic equations. We also proved norm estimates of these solutions.
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