2009 Fiscal Year Final Research Report
Study on differential equations arising out of life phenomena in vivo
| Project/Area Number |
19540200
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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 | Fujita Health University |
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Principal Investigator |
KUBO Akisato Fujita Health University, 医療科学部, 教授 (60170023)
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| Co-Investigator(Renkei-kenkyūsha) |
UMEZAWA Eizou 藤田保健衛生大学, 医療科学部, 准教授 (50318359)
SAITO Norikazu 東京大学, 大学院・数理科学研究科, 准教授 (00334706)
TESHIMA Kyuzo お茶の水女子大学, 大学院・人間文化創成科学研究科研究院, 研究員 (70288471)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 生命現象 / 数理モデル / 数学解析 / 腫瘍の成長 / 腫瘍の侵潤 / 腫瘍血管新生 / 非線形発展方程式 / 時間大域解 |
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| Research Abstract |
(1) We invited Professor M.Chaplain from Dundee University, UK to Japan for a week, September, 2007. On this occasion we organized the international conference" "Workshop on Mathematical Modelling and Analysis of Biological Pattern Formations and the Related Topics" (25-26, September, Nagoya University) (http://www.fujita-hu.ac.jp/~akikubo/).
(2) We investigated mathematical model of tumour growth and invasion by M.Chaplain and G.Lolas, 2006. The principal investigator and co-investigators have to spend much time to overcome this difficulty.
(3) We succeeded to obtain the mathematically exact relation between Othmer and Stevens model and Anderson and Chaplain model of tumour induced angiogenesis. Our result allow us to connect them from one to another only by formal calculation and substitution.
(4) We tried to improve our mathematical way used in a sequence of mathematical models of tumour angiogenesis and tumour invasion by Anderson and Chaplain in order to study the latest model of nonlocal tumour invasion by Gerish and Chaplain (2007).
2009
(5) The principal investigator and co-investigators of this project studied an initial 0-Neumann boundary problem of nonlinear evolution equations in more general frame work. Finally to complete touch to this project we could give a characterization of a sequence of tumour growth models studied in this project by this framework of existence theorem and properties of the solution of our nonlinear evolution equations(see research activities 1,2,3).
(6) The main investigator and his collaborator applied the method used by Levine and Sleeman (1998) in initial Neumann boundary value problems of the evolution equation and succeeded to show the existence of blow up solution under Dirichlet boundary condition(see research activities 4)
(7) Based on the mathematical analysis in (2)to (6), we made computer simulations for each problem.
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Research Products
(19 results)
