Study of quasilinear degenerate Keller-Segel systems and complex Ginzburg-Landau type equations'

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400119
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tokyo University of Science
• Principal Investigator: Yokota Tomomi 東京理科大学, 理学部, 准教授 (60349826)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 解の存在 / 解の漸近挙動 / ケラー・シーゲル系 / 複素ギンツブルク・ランダウ方程式

Outline of Final Research Achievements

In this research, we made mathematical analysis to ``Global-in-time solvability and asymptotic behavior of solutions in quasilinear degenerate Keller-Segel systems'' and `` Global-in-time solvability and asymptotic behavior of solutions in complex Ginzburg-Landau type equations'' as main themes.　The equations dealt with in these two themes are formally different, but there is a common in terms of parabolic equations. As to the former theme, we not only succeeded in showing boundedness of solutions left as an open problem but also obtained the same results for related equations. As to the latter theme, we succeeded in obtaining a precise result on blow-up and extinction of solutions.

Free Research Field

関数解析・発展方程式