Well-posedness for nonautonomous differential systems with dissipativity structure described by metric-like functionals

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400134
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Shizuoka University
• Principal Investigator: TANAKA Naoki 静岡大学, 理学部, 教授 (00207119)
• Co-Investigator(Kenkyū-buntansha): SHIMIZU Senjo 京都大学, 人間・環境学研究科, 教授 (50273165) ; ISHII Katsuyuki 神戸大学, 海事科学研究科, 教授 (40232227)
• Co-Investigator(Renkei-kenkyūsha): MATSUMOTO Toshitaka 静岡大学, 理学部, 教授 (20229561)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: evolution operator / metric-like functional / connectedness condition / subtangential condition / dissipativity condition / monotone operator / Lipschitz semigroup / comparison function

Outline of Final Research Achievements

We characterize the well-posedness for nonautonomous differential equations governed by continuous operators, using dissipativity conditions with respect to metric-like functionals, subtangential conditions and connectedness conditions. Toward to the non-continuous case, we generalize the cerebrated well-posedness result on autonomous differential equations governed by maximal monotone operators due to Komura and Brezis. Moreover, we discuss the well-posedness for functional differential equations and the solvability of abstract Cauchy problems for weakly continuous operators.

Free Research Field

実解析学（作用素半群の理論と発展方程式）