| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
Nonlinear parabolic partial differential equations are used in mathematical models to describe taxis phenomena arising from physics, chemistry, biology and other fields of natural scences. Since analytic solutions can not be obtained in general, it is an important research theme to get highly accurate numerical solutions which contribute to the development of those fields of natural scences. In this research project, the representative investigates Keller-Segel type problems on unbounded domains and, by successfully obtaining the approximate problems on bounded domains, develops validate methods to solve numerically blow-up solutions. By applying the proposed numerical technique, the representative develops high order numerical methods to elliptic partial differential equations with singular solutions, and Rossby solitary waves excited by the unstable topography in weak shear flow.
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