Mendeley出力
＜博士論文＞
反応拡散方程式系におけるパターン形成に対する計算機援用証明
| 作成者 | |
|---|---|
| 本文言語 | |
| 学位授与年度 | |
| 学位授与大学 | |
| 学位 | |
| 学位種別 | |
| 出版タイプ | |
| アクセス権 | |
| JaLC DOI | |
| 概要 | In this paper we give a method by computer-assistance to prove a pattern formation. As a typical model we consider two dimensional time-dependent reaction-diffusion equations with Neumann boundary con...ditions. For suitable system parameters we solve (approximately) the parabolic problem, hoping for some convergence to some pattern formation stationary (approximate) solution, and improve the approximation to a stationary solution by Newton's method, then enclose the stationary solution by our numerical verification method. Next we prove that the operator linearized at the exact stationary solution is a sectorial operator and compute a bound for the resolvent of the linearized operator which is needed for semigroup estimates. By using the semigroup estimate we analytically compute a domain of attraction for the stationary solution, i.e. some (norm-)neighborhood of the stationary solution such that, for initial data within this neighborhood, the parabolic solution converges to the stationary solution. For suitable initial conditions, if we enclose the solution of the parabolic problem until, for some time T, the enclosing set is a subset of the domain of attraction, then we can conclude that from time T on, convergence to the stationary solution takes place. This gives a complete convergence result, proving a pattern formation, for the initial conditions used for the parabolic problem.続きを見る |
| 目次 | Abstract 1 Introduction 2 Some notations and projection error estimation 3 Approximate solution 4 Veri cation 5 Eigenvalue excluding 6 The domain of attraction 7 Numerical Results 8 Conclusions Acknowledgements References続きを見る |
本文ファイル
| ファイル | ファイルタイプ | サイズ | 閲覧回数 | 説明 |
|---|---|---|---|---|
math143
|
974 KB | 326 | 本文 | |
|
math143_abstract
|
9.77 KB | 154 | 要旨 |
詳細
| レコードID | |
|---|---|
| 査読有無 | |
| キーワード | |
| 報告番号 | |
| 学位記番号 | |
| 授与日(学位/助成/特許) | |
| 受理日 | |
| 部局 | |
| 所蔵場所 | |
| 所蔵場所 | |
| 所在記号 | |
| 注記 | |
| 登録日 | 2013.07.12 |
| 更新日 | 2023.11.21 |