Asymptotic Analysis of quasilinear ordinary differential equations and its application to asymptotic analysis of elliptic equations

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540196
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Gifu University
• Principal Investigator: USAMI Hiroyuki 岐阜大学, 工学部, 教授 (90192509)
• Co-Investigator(Renkei-kenkyūsha): NAITO Manabu 愛媛大学, 大学院理工学研究科, 教授 (00106791) ; KAMO Ken-ichi 札幌医科大学, 医療人育成センター, 准教授 (10404740) ; TANIGAWA Tomoyuki 熊本大学, 教育学部, 准教授 (10332008) ; TERAMOTO Tomomitsu 尾道大学, 経済情報学部, 助教 (20398465)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 常微分方程式 / 漸近挙動 / 波動方程式 / 逆問題

Outline of Final Research Achievements

(1) We found the asymptotic forms of solutions of quasilinear ordinary differential equations. In particular, we found asymptotic behavior of positive solutions belonging to classes of Karamata functions under considerably weak assumptions. We could also find existence results for so-called intermediate growth solutions. Finally, we could solve inverse problems concerning to blow-up times.
(2) We could analyze linear hyperbolic equations with damping terms based on Fourier Analysis. In order to examine asymptotic behavior of solutions of reaction-diffusion systems, we analyzed Lanchester type ordinary differential systems. We found that, as in the classical systems, there are critical values for initial data classifying asymptotic behavior of solutions essentially.

Free Research Field

微分方程式