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解析学火曜セミナー
過去の記録 ～09/18｜次回の予定｜今後の予定 09/19～
| 開催情報 | 火曜日 16:00～17:30 数理科学研究科棟(駒場) 156号室 |
|---|---|
| 担当者 | 石毛 和弘, 坂井 秀隆, 伊藤 健一 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/analysis/ |
2022年04月12日(火)
16:00-17:30 オンライン開催
Amru Hussein 氏 (Technische Universität Kaiserslautern)
Maximal $L^p$-regularity and $H^{\infty}$-calculus for block operator matrices and applications (English)
https://forms.gle/QbQKex12dbQrt2Lw6
Amru Hussein 氏 (Technische Universität Kaiserslautern)
Maximal $L^p$-regularity and $H^{\infty}$-calculus for block operator matrices and applications (English)
[ 講演概要 ]
Many coupled evolution equations can be described via $2\times2$-block operator matrices of the form $\mathcal{A}=\begin{bmatrix}A & B \\ C & D \end{bmatrix}$ in a product space $X=X_1\times X_2$ with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator $\mathcal{A}$ can be seen as a relatively bounded perturbation of its diagonal part though with possibly large relative bound. For such operators, the properties of sectoriality, $\mathcal{R}$-sectoriality and the boundedness of the $H^\infty$-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time-dependent parabolic problem associated with $\mathcal{A}$ can be analyzed in maximal $L^p_t$-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.
This talk is based on a joint work with Antonio Agresti, see https://arxiv.org/abs/2108.01962
[ 参考URL ]Many coupled evolution equations can be described via $2\times2$-block operator matrices of the form $\mathcal{A}=\begin{bmatrix}A & B \\ C & D \end{bmatrix}$ in a product space $X=X_1\times X_2$ with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator $\mathcal{A}$ can be seen as a relatively bounded perturbation of its diagonal part though with possibly large relative bound. For such operators, the properties of sectoriality, $\mathcal{R}$-sectoriality and the boundedness of the $H^\infty$-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time-dependent parabolic problem associated with $\mathcal{A}$ can be analyzed in maximal $L^p_t$-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.
This talk is based on a joint work with Antonio Agresti, see https://arxiv.org/abs/2108.01962
https://forms.gle/QbQKex12dbQrt2Lw6
