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Applied Analysis
Seminar information archive ～09/27｜Next seminar｜Future seminars 09/28～
| Date, time & place | Thursday 16:00 - 17:30 002Room #002 (Graduate School of Math. Sci. Bldg.) |
|---|
Seminar information archive
2006/12/14
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
山田 澄生 (東北大・大学院理学研究科・理学部
数学専攻)
特異点を持つ極小部分多様体の変分原理
山田 澄生 (東北大・大学院理学研究科・理学部
数学専攻)
特異点を持つ極小部分多様体の変分原理
[ Abstract ]
与えられた境界を持つ極小部分集合に特異点が必然的に現れることは
今までによく知られている現象である。幾何学的測度論は、それらの特異点
を許容する存在定理の枠組みを提供する為に発展してきた。こうして
現れる部分集合の幾何学的特徴付けを、写像の持つエネルギー関数の最小化というJ.Douglas
の方法論を発展させることによって試みる。また特異点周辺の面積密度の
単調性公式についても言及したい。
与えられた境界を持つ極小部分集合に特異点が必然的に現れることは
今までによく知られている現象である。幾何学的測度論は、それらの特異点
を許容する存在定理の枠組みを提供する為に発展してきた。こうして
現れる部分集合の幾何学的特徴付けを、写像の持つエネルギー関数の最小化というJ.Douglas
の方法論を発展させることによって試みる。また特異点周辺の面積密度の
単調性公式についても言及したい。
2006/12/14
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
山田 澄生
(東北大学・大学院理学研究科)
特異点を持つ極小部分多様体の変分原理
山田 澄生
(東北大学・大学院理学研究科)
特異点を持つ極小部分多様体の変分原理
[ Abstract ]
与えられた境界を持つ極小部分集合に特異点が必然的に現れることは今までによく知られている現象である.幾何学的測度論は,それらの特異点を許容する存在定理の枠組みを提供する為に発展してきた.こうして現れる部分集合の幾何学的特徴付けを,写像の持つエネルギー関数の最小化というJ.Douglas の方法論を発展させることによって試みる.また特異点周辺の面積密度の単調性公式についても言及したい.
与えられた境界を持つ極小部分集合に特異点が必然的に現れることは今までによく知られている現象である.幾何学的測度論は,それらの特異点を許容する存在定理の枠組みを提供する為に発展してきた.こうして現れる部分集合の幾何学的特徴付けを,写像の持つエネルギー関数の最小化というJ.Douglas の方法論を発展させることによって試みる.また特異点周辺の面積密度の単調性公式についても言及したい.
2006/11/21
16:30-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Henrik SHAHGHOLIAN (王立工科大学、ストックホルム)
Composite membrane and the structure of the singular set
Henrik SHAHGHOLIAN (王立工科大学、ストックホルム)
Composite membrane and the structure of the singular set
[ Abstract ]
In this talk we present our study of the behavior of the singular set
$\\{u=|\\nabla u| =0\\}$ for solutions $u$ to the free boundary problem
$$
\\Delta u = f\\chi_{\\{u\\geq 0\\} } -g\\chi_{\\{u<0\\}},
$$
where $f$ and $g$ are H\\"older continuous functions, $f$ is positive and $f+g$ is negative. Such problems arise in an eigenvalue optimization for composite membranes.
We show that if for a singular point $z$ there are $r_0>0$, and $c_0>0$ such that the density assumption
$|\\{u< 0\\}\\cap B_r(z)|\\geq c_0 r2 \\forall r< r_0$
holds, then $z$ is isolated.
In this talk we present our study of the behavior of the singular set
$\\{u=|\\nabla u| =0\\}$ for solutions $u$ to the free boundary problem
$$
\\Delta u = f\\chi_{\\{u\\geq 0\\} } -g\\chi_{\\{u<0\\}},
$$
where $f$ and $g$ are H\\"older continuous functions, $f$ is positive and $f+g$ is negative. Such problems arise in an eigenvalue optimization for composite membranes.
We show that if for a singular point $z$ there are $r_0>0$, and $c_0>0$ such that the density assumption
$|\\{u< 0\\}\\cap B_r(z)|\\geq c_0 r2 \\forall r< r_0$
holds, then $z$ is isolated.
2006/11/16
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
奈良 光紀 (東京工業大学)
The large time behavior of graphical surfaces in the mean curvature flow
奈良 光紀 (東京工業大学)
The large time behavior of graphical surfaces in the mean curvature flow
[ Abstract ]
We are interested in the large time behavior of a surface in the whole space moving by the mean curvature flow. Studying the Cauchy problem on $R^{N}$, we deal with moving surfaces represented by entire graphs. We focus on the case of $N=1$ and the case of $N\\geq2$ with radially symmetric surfaces. We show that the solution converges uniformly to the solution of the Cauchy problem of the heat equation, if the initial value is bounded. Our results are based on the decay estimates for the derivatives of the solution. This is a joint work with Prof. Masaharu Taniguchi of Tokyo Institute of Technology.
We are interested in the large time behavior of a surface in the whole space moving by the mean curvature flow. Studying the Cauchy problem on $R^{N}$, we deal with moving surfaces represented by entire graphs. We focus on the case of $N=1$ and the case of $N\\geq2$ with radially symmetric surfaces. We show that the solution converges uniformly to the solution of the Cauchy problem of the heat equation, if the initial value is bounded. Our results are based on the decay estimates for the derivatives of the solution. This is a joint work with Prof. Masaharu Taniguchi of Tokyo Institute of Technology.
2006/11/02
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Messoud Efendiev (ミュンヘン工科大学)
On attractor of Swift-Hohenberg equation in unbounded domain and its Kolmogorov entropy
Messoud Efendiev (ミュンヘン工科大学)
On attractor of Swift-Hohenberg equation in unbounded domain and its Kolmogorov entropy
[ Abstract ]
The main objective of the talk is to give a description of the large-time behaviour of solutions of the Swift-Hohenberg equation in unbounded domain.This will be done in terms of the global attractor. Here we encounter serious difficulties due to the lack of compactness of the embedding theorems and the interplay between the different topologies will play crucial role.We prove the existence of the global attractor and show that the restriction of the attractor to any bounded sets has an infinite fractal dimension and present sharp estimate for its Kolmogorov entropy.Spatio-temporal chaotic dynamics on the attractor will also be discussed.
The main objective of the talk is to give a description of the large-time behaviour of solutions of the Swift-Hohenberg equation in unbounded domain.This will be done in terms of the global attractor. Here we encounter serious difficulties due to the lack of compactness of the embedding theorems and the interplay between the different topologies will play crucial role.We prove the existence of the global attractor and show that the restriction of the attractor to any bounded sets has an infinite fractal dimension and present sharp estimate for its Kolmogorov entropy.Spatio-temporal chaotic dynamics on the attractor will also be discussed.
2006/06/15
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Mark Bowen (東京大学大学院数理科学研究科/日本学術振興会)
Spreading and draining in thin fluid films
Mark Bowen (東京大学大学院数理科学研究科/日本学術振興会)
Spreading and draining in thin fluid films
[ Abstract ]
The surface tension driven flow of a thin fluid film arises in a number of contexts. In this talk, we will begin with an overview of thin film theory and present a number of examples from the natural sciences and industrial process engineering. Similarity solutions play an important role in understanding the dynamics of general thin film motion and we shall use them to investigate the dynamics of an archetypal (degenerate high-order parabolic) thin film equation. In this context, we will encounter self-similarity of the first and second kind, undertake an investigation of a four-dimensional phase space and discover a surprisingly rich set of stable sign-changing solutions for the intermediate asymptotics of a generalised problem.
The surface tension driven flow of a thin fluid film arises in a number of contexts. In this talk, we will begin with an overview of thin film theory and present a number of examples from the natural sciences and industrial process engineering. Similarity solutions play an important role in understanding the dynamics of general thin film motion and we shall use them to investigate the dynamics of an archetypal (degenerate high-order parabolic) thin film equation. In this context, we will encounter self-similarity of the first and second kind, undertake an investigation of a four-dimensional phase space and discover a surprisingly rich set of stable sign-changing solutions for the intermediate asymptotics of a generalised problem.
2006/06/07
16:00-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Marek FILA (Bratislava, スロバキア) 16:00-17:00
Slow convergence to zero for a supercritical parabolic equation
柴田 良弘 (早稲田大学・理工学部数理科学科) 17:00-18:00
未定
Marek FILA (Bratislava, スロバキア) 16:00-17:00
Slow convergence to zero for a supercritical parabolic equation
柴田 良弘 (早稲田大学・理工学部数理科学科) 17:00-18:00
未定
2006/05/18
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
石井 仁司 (早稲田大学 教育学部 理学科 数学専修)
Asymptotic behavior for large-time of solutions of Hamilton-Jacobi equations in n space
石井 仁司 (早稲田大学 教育学部 理学科 数学専修)
Asymptotic behavior for large-time of solutions of Hamilton-Jacobi equations in n space
2006/04/27
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
西原 健二 (早稲田大学・政治経済学術院)
消散型波動方程式のコーシー問題の解の挙動
西原 健二 (早稲田大学・政治経済学術院)
消散型波動方程式のコーシー問題の解の挙動
