| Project/Area Number |
15540145
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Fujita Health University College |
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Principal Investigator |
HOSHINO Hiroki Fujita Health University College, Department of Medical Technology, Associate Professor, 衛生技術科, 助教授 (80238740)
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| Co-Investigator(Kenkyū-buntansha) |
KUBO Akisato Fujita Health University, Faculty of Health Sciences, Professor, 衛生学部, 教授 (60170023)
ISHII Katsuyuki Kobe University, Faculty of Maritime Sciences, Associate Professor, 海事科学部, 助教授 (40232227)
NAITO Morihiro Fujita Health University College, Department of Medical Technology, Associate Professor, 衛生技術科, 助教授 (80132257)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2003: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | reaction-diffusion system / tumor angiogenesis / Lyapunov function / behavior of solutions / simulation / 不連続非線型項 / 進行波 / 血管新生 |
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| Research Abstract |
H.Hoshino studied reaction-diffusion systems for the model of tumor angiogenesis presented by Othmer and Stevens in 1997 and Anderson and Chaplain in 1998 with A.Kubo and T.Suzuki (Osaka University). Hoshino showed the well-posedness in the Holder spaces of the solutions to the systems and the existence of Lyapunovfunctions. Moreover, by numerical simulations, he obtained the animations for the discrete models of angiogenesis by the Monte Carlo method and those for the continuous models by the finite element method.
A.Kubo constructed global solutions to the degenerate hyperbolic equations derived from the model of tumorangiogenesis and investigated their asymptotic behavior. Especially, he considered the cases where initial functions have small perturbations from constant states and applied Galerkin's method to get the results.
K.Ishii investigated the convergence of the algorithm for computing the motion of a hypersurface by mean curvature flow given by Bence, Merriman and Osher. He obtained the convergence rate of the algorithm for the motion of a smooth and compact hypersurface by mean curvature. Furthermore, he considered the specialcase of a circle evolving by curvature and showed that the rate is optimal.
With Proteus mirabilis having active motility, M.Naito observed that how its motility depends on conditions of culture mediums, and he investigated whether the difference of the states of mediums (e.g., solid or semi-solid mediums) or of the temperature of culture would give that of the motility or not. By this observation, he considered the validity of mathematical models with discontinuous nonlinear term describing the growth of bacteria.
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