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過去の記録 ～04/23｜次回の予定｜今後の予定 04/24～
| 開催情報 | 木曜日 16:00～17:30 数理科学研究科棟(駒場) 002号室 |
|---|---|
| 担当者 | 石毛 和弘 |
過去の記録
2007年04月05日(木)
16:00-17:30 数理科学研究科棟(駒場) 126号室
Robert P. GILBERT 氏 (デラウェア大学・数学教室)
Acoustic Modeling and Osteoporotic Evaluation of Bone
Robert P. GILBERT 氏 (デラウェア大学・数学教室)
Acoustic Modeling and Osteoporotic Evaluation of Bone
[ 講演概要 ]
In this talk we discuss the modeling of the acoustic response of cancellous bone using the methods of homogenization.
This can lead to Biot type equations or more generalized equations. We develop the effective acoustic equations for cancellous bone. It is assumed that the bone matrix is elastic and the interstitial blood-marrow can be modeled as a Navier-Stokes system.
We also discuss the use of the Biot model and consider its applicability to cancellous bone. One of the questions this talk addresses is whether the clinical experiments customarily performed can be used to determine the parameters of the Biot or other bone models. A parameter recovery algorithm which uses parallel processing is developed and tested.
In this talk we discuss the modeling of the acoustic response of cancellous bone using the methods of homogenization.
This can lead to Biot type equations or more generalized equations. We develop the effective acoustic equations for cancellous bone. It is assumed that the bone matrix is elastic and the interstitial blood-marrow can be modeled as a Navier-Stokes system.
We also discuss the use of the Biot model and consider its applicability to cancellous bone. One of the questions this talk addresses is whether the clinical experiments customarily performed can be used to determine the parameters of the Biot or other bone models. A parameter recovery algorithm which uses parallel processing is developed and tested.
2007年02月16日(金)
15:00-16:00 数理科学研究科棟(駒場) 056号室
* 曜日と時間が普段と異なりますのでご注意ください.
Ratnasingham SHIVAJI 氏 (ミシシッピ州立大学)
Multiple positive solutions for classes of elliptic systems with combined nonlinear effects
* 曜日と時間が普段と異なりますのでご注意ください.
Ratnasingham SHIVAJI 氏 (ミシシッピ州立大学)
Multiple positive solutions for classes of elliptic systems with combined nonlinear effects
[ 講演概要 ]
We study the existence of multiple positive solutions to systems of the form
-\\Delta u = \\lambda f(v)
-\\Delta v = \\lambda g(u)
in a bounded domain in R^N under the Dirichlet boundary conditions. Here f, g belong to a class of positive functions having a combined sublinear effect at infinity. Our result also easily extends to the corresponding p-Laplacian systems. We prove our results by the method of sub and super solutions.
We study the existence of multiple positive solutions to systems of the form
-\\Delta u = \\lambda f(v)
-\\Delta v = \\lambda g(u)
in a bounded domain in R^N under the Dirichlet boundary conditions. Here f, g belong to a class of positive functions having a combined sublinear effect at infinity. Our result also easily extends to the corresponding p-Laplacian systems. We prove our results by the method of sub and super solutions.
2007年01月25日(木)
16:00-17:30 数理科学研究科棟(駒場) 056号室
Michael TRIBELSKY 氏 (東大・数理 / モスクワ工科大学)
Soft-mode turbulence as a new type of spatiotemporal chaos at onset
Michael TRIBELSKY 氏 (東大・数理 / モスクワ工科大学)
Soft-mode turbulence as a new type of spatiotemporal chaos at onset
2007年01月18日(木)
16:00-17:30 数理科学研究科棟(駒場) 056号室
LIANG Xing 氏 (東京大学大学院数理科学研究科 / 日本学術振興会)
Asymptotic Speeds of Spread and Traveling Waves for Monotone Semiflows with Applications
LIANG Xing 氏 (東京大学大学院数理科学研究科 / 日本学術振興会)
Asymptotic Speeds of Spread and Traveling Waves for Monotone Semiflows with Applications
[ 講演概要 ]
The theory of asymptotic speeds of spread and monotone traveling waves is established for a class of monotone discrete and continuous-time semiflows and is applied to a functional differential equation with diffusion, a time-delayed lattice population model and a reaction-diffusion equation in an infinite
cylinder.
The theory of asymptotic speeds of spread and monotone traveling waves is established for a class of monotone discrete and continuous-time semiflows and is applied to a functional differential equation with diffusion, a time-delayed lattice population model and a reaction-diffusion equation in an infinite
cylinder.
2006年12月21日(木)
16:00-17:30 数理科学研究科棟(駒場) 056号室
Susan Friedlander 氏 (University of Illinois-Chicago)
An Inviscid Dyadic Model For Turbulence
Susan Friedlander 氏 (University of Illinois-Chicago)
An Inviscid Dyadic Model For Turbulence
[ 講演概要 ]
We discuss properties of a GOY type model for the inviscid fluid equations. We prove that the forced system has a unique equilibrium which a an exponential global attractor. Every solution blows up in H^5/6 in finite time . After this time, all solutions stay in H^s, s<5/6, and "turbulent" dissipation occurs. Onsager's conjecture is confirmed for the model system.
This is joint work with Alexey Cheskidov and Natasa Pavlovic.
We discuss properties of a GOY type model for the inviscid fluid equations. We prove that the forced system has a unique equilibrium which a an exponential global attractor. Every solution blows up in H^5/6 in finite time . After this time, all solutions stay in H^s, s<5/6, and "turbulent" dissipation occurs. Onsager's conjecture is confirmed for the model system.
This is joint work with Alexey Cheskidov and Natasa Pavlovic.
2006年12月14日(木)
16:00-17:30 数理科学研究科棟(駒場) 056号室
山田 澄生 氏 (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 氏 (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
[ 講演概要 ]
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年12月14日(木)
16:00-17:30 数理科学研究科棟(駒場) 056号室
山田 澄生
氏 (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
氏 (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
[ 講演概要 ]
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年11月21日(火)
16:30-17:30 数理科学研究科棟(駒場) 122号室
いつもの曜日・時間・セミナー室と違いますのでご注意ください
Henrik SHAHGHOLIAN 氏 (王立工科大学、ストックホルム)
Composite membrane and the structure of the singular set
いつもの曜日・時間・セミナー室と違いますのでご注意ください
Henrik SHAHGHOLIAN 氏 (王立工科大学、ストックホルム)
Composite membrane and the structure of the singular set
[ 講演概要 ]
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年11月16日(木)
16:00-17:30 数理科学研究科棟(駒場) 056号室
奈良 光紀 氏 (東京工業大学)
The large time behavior of graphical surfaces in the mean curvature flow
奈良 光紀 氏 (東京工業大学)
The large time behavior of graphical surfaces in the mean curvature flow
[ 講演概要 ]
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年11月02日(木)
16:00-17:30 数理科学研究科棟(駒場) 056号室
Messoud Efendiev 氏 (ミュンヘン工科大学)
On attractor of Swift-Hohenberg equation in unbounded domain and its Kolmogorov entropy
Messoud Efendiev 氏 (ミュンヘン工科大学)
On attractor of Swift-Hohenberg equation in unbounded domain and its Kolmogorov entropy
[ 講演概要 ]
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年06月15日(木)
16:00-17:30 数理科学研究科棟(駒場) 056号室
6月15日は,集中講義と重なるため,開始時間を遅らせます.
Mark Bowen 氏 (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
6月15日は,集中講義と重なるため,開始時間を遅らせます.
Mark Bowen 氏 (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
[ 講演概要 ]
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年06月07日(水)
16:00-18:00 数理科学研究科棟(駒場) 002号室
Marek FILA 氏 (Bratislava, スロバキア) 16:00-17:00
Slow convergence to zero for a supercritical parabolic equation
柴田 良弘 氏 (早稲田大学・理工学部数理科学科) 17:00-18:00
未定
Marek FILA 氏 (Bratislava, スロバキア) 16:00-17:00
Slow convergence to zero for a supercritical parabolic equation
柴田 良弘 氏 (早稲田大学・理工学部数理科学科) 17:00-18:00
未定
2006年05月18日(木)
16:00-17:30 数理科学研究科棟(駒場) 056号室
石井 仁司 氏 (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 氏 (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年04月27日(木)
16:00-17:30 数理科学研究科棟(駒場) 056号室
西原 健二 氏 (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 氏 (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
