Large time behaviors of solutions of nonlinear conservation laws with dissipative structures of energy

2014 Fiscal Year Final Research Report

• Project/Area Number: 23340036
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Osaka University
• Principal Investigator: MATSUMURA Akitaka 大阪大学, 情報科学研究科, 教授 (60115938)
• Co-Investigator(Kenkyū-buntansha): CHAWANYA Takeshi 大阪大学, 大学院情報科学研究科, 准教授 (80294148)
• Co-Investigator(Renkei-kenkyūsha): ODANAKA Shinji 大阪大学, サイバーメディアセンター, 教授 (20324858) ; NISHIHARA Kenji 早稲田大学, 政治経済学部, 教授 (60141876) ; NISHIBATA Shinya 東京工業大学, 大学院情報理工学研究科, 教授 (80279299) ; YANAGISAWA Taku 奈良女子大学, 大学院自然科学研究科, 教授 (30192389) ; TSUGE Naoki 岐阜大学, 教育学部, 准教授 (30449897) ; IOHARA Takao 大阪大学, 大学院理学研究科, 助教 (00294140) ; KAI Itsuko (HASHIMOTO Itsuko) 富山工業高等専門学校, 一般教育科, 准教授 (30449897)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Keywords: 粘性保存則 / 時間大域解 / 漸近挙動 / エネルギー法 / 圧縮性気体 / 非線形波動方程式 / 半導体方程式 / 大規模力学系

Outline of Final Research Achievements

Various weighted energy methods were successfully manipulated to have a priori estimates for solutions of nonlinear conservation laws with dissipative structures of energy. With the aid of these methods, has been much progressed the analysis on the large time behaviors of the solutions of scalar viscous conservation law with non-convex flux, system of equations of ideal gas, dissipative wave equations,　model system of semiconductor, large scale dynamical system, etc. As for a model system of semiconductor, which is very important in practical applications, an efficient method of numerical computation to get the stationary solutions was proposed.

Free Research Field

解析学