Stability analysis for nonlinear partial differential equations

2014 Fiscal Year Final Research Report

• Project/Area Number: 22244009
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: KAWASHIMA Shuichi 九州大学, 数理(科)学研究科(研究院), 教授 (70144631)
• Co-Investigator(Kenkyū-buntansha): KAGEI Yoshiyuki 九州大学, 大学院数理学研究院, 教授 (80243913) ; NAKAMURA Tohru 熊本大学, 大学院自然科学研究科, 准教授 (90432898) ; OGAWA Takayoshi 東北大学, 大学院理学研究科, 教授 (20224107) ; IKEHATA Ryo 広島大学, 大学院教育学研究科, 教授 (10249758)
• Co-Investigator(Renkei-kenkyūsha): KOBAYASHI Takayuki 大阪大学, 大学院基礎工学研究科, 教授 (50272133) ; HATAYA Yasushi 山口大学, 大学院理工学研究科, 助教 (20294621)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 偏微分方程式 / 消散構造 / 安定性解析 / 減衰評価 / エネルギー法

Outline of Final Research Achievements

We studied systems of nonlinear partial differential equations in the fields of gas dynamics, elasto-dynamics and plasma physics. We investigated the dissipative structure and decay property of the systems and proved the asymptotic stability of various nonlinear phenomena of vibration and wave propagation. Also we developed a general theory on nonlinear stability analysis for hyperbolic systems of conservation equations with relaxation and observed that the time-weighted energy method, semigroup approach and the technique of harmonic analysis are useful in the stability analysis.

Free Research Field

偏微分方程式