WEKO3
アイテム
Determining nodes for semilinear parabolic evolution equations in Banach spaces
https://doi.org/10.15083/00005563
https://doi.org/10.15083/000055633175cf57-e71e-4037-b259-164805ac028f
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
KakizawaR_24_3_PhD_a.pdf (3.0 MB)
|
|
|
|
KakizawaR_24_3_PhD_b.pdf (65.7 kB)
|
|
| Item type | 学位論文 / Thesis or Dissertation(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2014-02-24 | |||||
| タイトル | ||||||
| タイトル | Determining nodes for semilinear parabolic evolution equations in Banach spaces | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_46ec | |||||
| タイプ | thesis | |||||
| ID登録 | ||||||
| ID登録 | 10.15083/00005563 | |||||
| ID登録タイプ | JaLC | |||||
| その他のタイトル | ||||||
| その他のタイトル | バナッハ空間上の半線型放物型発展方程式に対する確定節点 | |||||
| 著者 |
Kakizawa, Ryohei
× Kakizawa, Ryohei |
|||||
| 著者別名 | ||||||
| 識別子Scheme | WEKO | |||||
| 識別子 | 11602 | |||||
| 姓名 | 柿澤, 亮平 | |||||
| 著者所属 | ||||||
| 著者所属 | 東京大学大学院数理科学研究科 | |||||
| 著者所属 | ||||||
| 著者所属 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| Abstract | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | We are concerned with the determination of the asymptotic behaviour of strong solutions to the initial-boundary value problem for general semilinear parabolic equations by the asymptotic behaviour of these strong solutions on a finite set. More precisely, if the asymptotic behaviour of the strong solution is known on a suitable finite set which is called determining nodes, then the asymptotic behaviour of the strong solution itself is entirely determined. We prove the above property by the energy method. Moreover, we are concerned with the determination of the asymptotic behaviour of mild solutions to the abstract initial value problem for semilinear parabolic evolution equations in Lp by the asymptotic behaviour of these mild solutions on a finite set. More precisely, if the asymptotic behaviour of the mild solution is known on determining nodes, then the asymptotic behaviour of the mild solution itself is entirely determined. Not only the asymptotic equivalence but also rate of monomial or exponential convergence can be clarified. We prove the above properties by the theory of analytic semigroups on Banach spaces. As an important application of sectorial operators, we give the linearized operator (Stokes operator) associated with the initial-boundary value problem for the Navier-Stokes equations in a multiply-connected bounded domain with the Navier-Dirichlet boundary condition. Furthermore, we study the asymptotic properties of stationary solutions to this problem. As for the existence and uniqueness, this problem has uniquely a stationary solution in (W2p)n satisfying Lp estimates for any n < p < ∞. The first result is obtained from resolvent estimates for the Stokes operator in L(p,σ) and the Banach fixed point theorem. On the asymptotic stability, the stationary solutions are asymptotically stable in L(p,σ) if they are small in (W1p)n. The second result is proved by the theory of analytic semigroups on Banach spaces. | |||||
| 書誌情報 | 発行日 2012-03-22 | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 410 | |||||
| 学位名 | ||||||
| 学位名 | 博士(数理科学) | |||||
| 学位 | ||||||
| 値 | doctoral | |||||
| 学位分野 | ||||||
| Mathematical Sciences (数理科学) | ||||||
| 学位授与機関 | ||||||
| 学位授与機関名 | University of Tokyo (東京大学) | |||||
| 研究科・専攻 | ||||||
| Graduate School of Mathematical Sciences (数理科学研究科) | ||||||
| 学位授与年月日 | ||||||
| 学位授与年月日 | 2012-03-22 | |||||
| 学位授与番号 | ||||||
| 学位授与番号 | 甲第28381号 | |||||
| 学位記番号 | ||||||
| 博数理第389号 | ||||||
