| Project/Area Number |
17H07302
|
|---|
| Research Category |
Grant-in-Aid for Research Activity Start-up
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Mathematical analysis
|
|---|
| Research Institution | Tokyo University of Marine Science and Technology (2018)
Fukuoka Institute of Technology (2017) |
|---|
Principal Investigator |
Mori Naofumi 東京海洋大学, 学術研究院, 准教授 (10803413)
|
|---|
| Research Collaborator |
Kawashima Shuichi
Racke Reinhard
|
|---|
| Project Period (FY) |
2017-08-25 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| Keywords | 非線形偏微分方程式 / 消散構造 / 安定性解析 / 緩和的双曲系 / Timoshenko 系 / Cattaneo 法則 / 時間大域解 / 減衰評価 / 解析学 |
|---|
| Outline of Final Research Achievements |
The Timoshenko system was considered by introducing Cattaneo's type heat conduction or memory, respectively. Consequently, their dissipative structures were well characterized and optimal decay estimates were shown. Besides, the global existence and uniqueness were obtained. Note that all of the results were proved under the minimal regularity assumption only on the small initial data.
Also, by generalized above results, the new stability condition was established, which could be applicable to more examples than any other condition.
|
| Academic Significance and Societal Importance of the Research Achievements |
新しい消散構造をもつ数理モデルの具体例には，身近で生活との関わりが深いものも多く含まれる。それにもかかわらず，これらのモデルに対しては統一的な解析方法が確立されておらず，しかも消散効果が脆弱なため，数学的に厳密に議論するのが難しいという問題点がある。
今回得られた研究成果は，今後，これらの数理モデルの統一的な解析方法の確立に向けた研究において必要不可欠の結果になると考えている。
|
