Study on partial differential equations describing multi-scale life phenomenon

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400148
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Fujita Health University
• Principal Investigator: KUBO Akisato 藤田保健衛生大学, 保健学研究科, 教授 (60170023)
• Co-Investigator(Kenkyū-buntansha): UMEZAWA EIZOU 藤田保健衛生大学, 医療科学部, 准教授 (50318359) ; HOSHINO HIROKI 藤田保健衛生大学, 医療科学部, 准教授 (80238740) ; HAYASHI NAOKI 藤田保健衛生大学, 医療科学部, 講師 (00549884)
• Co-Investigator(Renkei-kenkyūsha): SAITO NORIKAZU 東京大学, 大学院数理科学研究科, 准教授 (00334706)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: マルチスケール / 非局所 / 腫瘍浸潤 / 腫瘍成長 / 数理モデル / 解の存在 / 漸近挙動 / シミュレーション

Outline of Final Research Achievements

The mathematical models of tumor growth and invasion proposed by Chaplain et al. consistently preserves a multi-scaling structure. In this research subject we consider Chaplain-Lolas and Gerisch-Chaplain models specified in this point of view clearly.
(1)We first completed mathematical analysis of the former and then in the same line we sutudied the latter. We could show the time global existence and asymptotic behavior of the solution of the former in the original form. (2)However, in the latter we found the non-local term is not well-defined on the boundary, and Chaplain has finally accepted this point in his latest paper, and gave biological justification. When it was known, we have already gone into the last year of the subject research period, and cannot help considering it as the future one. (3)We have confirmed some visualization of the behavior of Glioma cells in the invisible area of invasive range by computer simulations, based on experiments in vitro.

Free Research Field

関数方程式