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過去の記録
過去の記録 ～05/18｜本日 05/19 | 今後の予定 05/20～
2005年05月09日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
林本厚志 氏 (長野高専)
レビ形式が退化する、あるクラスの実超曲面の定義関数について
林本厚志 氏 (長野高専)
レビ形式が退化する、あるクラスの実超曲面の定義関数について
2005年04月25日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
藤川英華 氏 (東工大情報理工)
停留的写像類群とタイヒミュラー空間への作用
藤川英華 氏 (東工大情報理工)
停留的写像類群とタイヒミュラー空間への作用
2005年04月20日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
酒井 良 氏 (都立大学)
Small modifications of quadrature domains around a cusp
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
酒井 良 氏 (都立大学)
Small modifications of quadrature domains around a cusp
[ 講演概要 ]
A flow which is produced by injection of fluid into the narrow gap between two parallel planes is called a Hele-Shaw flow. We regard the flow as an increasing family of plane domains and discuss the case that the initial domain has a cusp on the boundary. We give sufficient conditions for the cusp to be a laminar-flow point.
[ 参考URL ]A flow which is produced by injection of fluid into the narrow gap between two parallel planes is called a Hele-Shaw flow. We regard the flow as an increasing family of plane domains and discuss the case that the initial domain has a cusp on the boundary. We give sufficient conditions for the cusp to be a laminar-flow point.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年04月18日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
厚地 淳 氏 (慶大経済)
エネルギー有限な有理形関数の除外点の個数について
厚地 淳 氏 (慶大経済)
エネルギー有限な有理形関数の除外点の個数について
2005年03月23日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 122号室
Helmut Abels 氏 (Max Planck Institute)
Pseudodifferential Boundary Value Problems with Non-Smooth Coefficients
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Helmut Abels 氏 (Max Planck Institute)
Pseudodifferential Boundary Value Problems with Non-Smooth Coefficients
[ 講演概要 ]
We discuss an operator class that models elliptic differential boundary value problems as well as their solution operators and is closed under compositions. It was introduced by Boutet de Monvel in 1971 and provides a powerful tool to calculate with symbols associated to these operators. But the standard calculus and most of its further developments require that the symbols have smooth coefficient in the space and phase variable. We present some results which extend the calculus to symbols which have limited smoothness in the space variable. Such an extension is nescessary to apply the calculus to nonlinear partial differential boundary value problems and free boundary value problems.
[ 参考URL ]We discuss an operator class that models elliptic differential boundary value problems as well as their solution operators and is closed under compositions. It was introduced by Boutet de Monvel in 1971 and provides a powerful tool to calculate with symbols associated to these operators. But the standard calculus and most of its further developments require that the symbols have smooth coefficient in the space and phase variable. We present some results which extend the calculus to symbols which have limited smoothness in the space variable. Such an extension is nescessary to apply the calculus to nonlinear partial differential boundary value problems and free boundary value problems.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年03月02日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 270号室
Italo Capuzzo-Dolcetta 氏 (Universita di Roma) 10:30-11:30
The maximum principle in unbounded domains
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Antonio Siconolfi 氏 (Universita di Roma) 11:45-12:45
Aubry set and applications
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Italo Capuzzo-Dolcetta 氏 (Universita di Roma) 10:30-11:30
The maximum principle in unbounded domains
[ 講演概要 ]
The issue of the talk is the validity of the Weak Maximum Principle for functions u satisfying a second-order partial differential inequality of the form
(*) F(x,u,Du,D^2u) ≧ 0
in a domain A of the n-dimensional euclidean space.
The main result presented in the lecture is that for bounded above upper semicontinuous functions verifying
(*) in the viscosity sense, the inequality u≦ 0 on the boundary ∂A is propagated in the interior of the domain itself, under suitable conditions on F and A.
These conditions include ellipticity of F, a general geometric condition on the (possibly) unbounded domain A and a joint requirement involving the spread of A and the decay of first order terms at infinity.
This result, contained in I.C.D, A.Leoni, A.Vitolo "The Alexandrov-Bakelman-Pucci weak Maximum Principle for fully nonlinear equations in unbounded domains", to appear in Comm.in PDE's, extends previous results due to X.Cabré and L.Caffarelli-X.Cabré.
In the second part of the talk we present different versions of Weak Maximum Principle, namely for solutions growing exponentially fast of (*) in narrow domains and for solutions of
(**) F(x,u,Du,D^2u) + c(x)u ≧ 0
(c changing sign) in domains of small measure.
[ 参考URL ]The issue of the talk is the validity of the Weak Maximum Principle for functions u satisfying a second-order partial differential inequality of the form
(*) F(x,u,Du,D^2u) ≧ 0
in a domain A of the n-dimensional euclidean space.
The main result presented in the lecture is that for bounded above upper semicontinuous functions verifying
(*) in the viscosity sense, the inequality u≦ 0 on the boundary ∂A is propagated in the interior of the domain itself, under suitable conditions on F and A.
These conditions include ellipticity of F, a general geometric condition on the (possibly) unbounded domain A and a joint requirement involving the spread of A and the decay of first order terms at infinity.
This result, contained in I.C.D, A.Leoni, A.Vitolo "The Alexandrov-Bakelman-Pucci weak Maximum Principle for fully nonlinear equations in unbounded domains", to appear in Comm.in PDE's, extends previous results due to X.Cabré and L.Caffarelli-X.Cabré.
In the second part of the talk we present different versions of Weak Maximum Principle, namely for solutions growing exponentially fast of (*) in narrow domains and for solutions of
(**) F(x,u,Du,D^2u) + c(x)u ≧ 0
(c changing sign) in domains of small measure.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Antonio Siconolfi 氏 (Universita di Roma) 11:45-12:45
Aubry set and applications
[ 講演概要 ]
For given Hamiltonian H(x, p) continuous and quasiconvex in the second argument, defined in Rn × Rn or on the cotangent bundle of a compact boundaryless manifold, we consider the equation
H= c
with c critical value, i.e. for which the equation admits locally Lipschitzcontinuous a.e. subsolutions, but not strict subsolutions. We show that there is a subset of the state variable space, called Aubry set and denoted by A, where the obstruction to the existence of such subsolutions is concentrated. We give a metric characterization of A, and we discuss its main properties.
They are applied to a projection problem in a Banach space, to the study of the largetime behaviour of subsolutions to a timedependent HamiltonJacobi equation, and to construct a Lyapunov function for a perturbed dynamics, under suitable stability assumptions.
[ 参考URL ]For given Hamiltonian H(x, p) continuous and quasiconvex in the second argument, defined in Rn × Rn or on the cotangent bundle of a compact boundaryless manifold, we consider the equation
H= c
with c critical value, i.e. for which the equation admits locally Lipschitzcontinuous a.e. subsolutions, but not strict subsolutions. We show that there is a subset of the state variable space, called Aubry set and denoted by A, where the obstruction to the existence of such subsolutions is concentrated. We give a metric characterization of A, and we discuss its main properties.
They are applied to a projection problem in a Banach space, to the study of the largetime behaviour of subsolutions to a timedependent HamiltonJacobi equation, and to construct a Lyapunov function for a perturbed dynamics, under suitable stability assumptions.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年01月26日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 122号室
Matthias Hieber 氏 (ダルムシュタット工科大学)
L^p-Theory of the Navier-Stokes flow past rotating or moving obstacles
Matthias Hieber 氏 (ダルムシュタット工科大学)
L^p-Theory of the Navier-Stokes flow past rotating or moving obstacles
[ 講演概要 ]
In this talk we consider the equation of Navier-Stokes in the exterior of a rotating or moving domain. Using techniques from the analysis of Ornstein-Uhlenbeck operators it is shown that, after rewriting the problem on a fixed domain $\\Omega$, the solution of the linearized equation is governed by a $C_0$-semigroup on $L^p_\\sigma(\\Omega)$ for $1
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
In this talk we consider the equation of Navier-Stokes in the exterior of a rotating or moving domain. Using techniques from the analysis of Ornstein-Uhlenbeck operators it is shown that, after rewriting the problem on a fixed domain $\\Omega$, the solution of the linearized equation is governed by a $C_0$-semigroup on $L^p_\\sigma(\\Omega)$ for $1
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005年01月24日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
金子 宏 氏 (東京理科大)
Hausdorff measure and exceptional sets in Dirichlet space theory on local fields
金子 宏 氏 (東京理科大)
Hausdorff measure and exceptional sets in Dirichlet space theory on local fields
2005年01月17日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
中川健治 氏 (長岡技術科学大学)
複素函数論の情報ネットワーク特性評価への応用
中川健治 氏 (長岡技術科学大学)
複素函数論の情報ネットワーク特性評価への応用
[ 講演概要 ]
情報ネットワークの特性評価を目的として,離散型 および連続型確率変数 X の裾確率 P(X > x) の指数的 減少について調べる。特に X が連続型の場合,X の確率 分布関数 F(x) = P(X ≧ x)のLaplace-Stieltjes変換を φ(s) とし,φ(s) の収束座標を σ とする。 -∞ < σ < 0 を仮定する。φ(s) の収束軸上の 特異点が高々有限個の極のみならば P(X > x) が指数的に 減少することを示す。その解析のために Ikehara による Tauber 型定理を拡張して適用する。
情報ネットワークの特性評価を目的として,離散型 および連続型確率変数 X の裾確率 P(X > x) の指数的 減少について調べる。特に X が連続型の場合,X の確率 分布関数 F(x) = P(X ≧ x)のLaplace-Stieltjes変換を φ(s) とし,φ(s) の収束座標を σ とする。 -∞ < σ < 0 を仮定する。φ(s) の収束軸上の 特異点が高々有限個の極のみならば P(X > x) が指数的に 減少することを示す。その解析のために Ikehara による Tauber 型定理を拡張して適用する。
2004年12月17日(金)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 126号室
D. Popovici 氏 (Warwick)
A simple proof of a theorem by Uhlenbeck and Yau
D. Popovici 氏 (Warwick)
A simple proof of a theorem by Uhlenbeck and Yau
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 126号室
Min Ru 氏 (Houston)
Holomorphic curves into algebraic varieties
Min Ru 氏 (Houston)
Holomorphic curves into algebraic varieties
2004年12月15日(水)
PDE実解析研究会
10:30-12:45 数理科学研究科棟(駒場) 122号室
Andrzej Swiech 氏 (ジョージア工科大学) 10:30-11:30
Hamilton-Jacobi-Bellman equations for optimal control of stochastic Navier-Stokes equations.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Francesca Da Lio 氏 (Dipartimento di Matematica P. e A.Universit di Padova researcher) 11:45-12:45
A GEOMETRICAL APPROACH TO FRONT PROPAGATION PROBLEMS IN BOUNDED DOMAINS WITH NEUMANN-TYPE BOUNDARY AND APPLICATIONS
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Andrzej Swiech 氏 (ジョージア工科大学) 10:30-11:30
Hamilton-Jacobi-Bellman equations for optimal control of stochastic Navier-Stokes equations.
[ 講演概要 ]
We consider a parameterized family of continuous functions, which containsas its members Bourbai's and Perkins's nowhere differentiable functions as well as the Cantor-Lebesgue singular functions.
[ 参考URL ]We consider a parameterized family of continuous functions, which containsas its members Bourbai's and Perkins's nowhere differentiable functions as well as the Cantor-Lebesgue singular functions.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Francesca Da Lio 氏 (Dipartimento di Matematica P. e A.Universit di Padova researcher) 11:45-12:45
A GEOMETRICAL APPROACH TO FRONT PROPAGATION PROBLEMS IN BOUNDED DOMAINS WITH NEUMANN-TYPE BOUNDARY AND APPLICATIONS
[ 講演概要 ]
We talk about a new definition of weak solution for the global-in-time motion of a front in bounded domains with normal velocity depending not only on its curvature but also on the measure of the set it encloses and with a contact angle boundary condition. We apply this definition to study the asymptotic behaviour of the solutions of some local and nonlocal reaction-diffusion equations.
[ 参考URL ]We talk about a new definition of weak solution for the global-in-time motion of a front in bounded domains with normal velocity depending not only on its curvature but also on the measure of the set it encloses and with a contact angle boundary condition. We apply this definition to study the asymptotic behaviour of the solutions of some local and nonlocal reaction-diffusion equations.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004年12月13日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 126号室
野口潤次郎 氏 (東大数理)
正則曲線、小林双曲性とアーベル多様体の川又特徴付け
野口潤次郎 氏 (東大数理)
正則曲線、小林双曲性とアーベル多様体の川又特徴付け
2004年12月01日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 122号室
岡本 久 氏 (京都大学)
A remark on continuous, nowhere differentiable functions
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
岡本 久 氏 (京都大学)
A remark on continuous, nowhere differentiable functions
[ 講演概要 ]
We consider a parameterized family of continuous functions, which containsas its members Bourbai's and Perkins's nowhere differentiable functions as well as the Cantor-Lebesgue singular functions.
[ 参考URL ]We consider a parameterized family of continuous functions, which containsas its members Bourbai's and Perkins's nowhere differentiable functions as well as the Cantor-Lebesgue singular functions.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004年10月20日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 122号室
Hermann Sohr 氏 (University of Paderborn)
Some recent results on the Navier-Stokes equations
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Hermann Sohr 氏 (University of Paderborn)
Some recent results on the Navier-Stokes equations
[ 講演概要 ]
The aim of this talk is to explain some new results in particular on local regularity properties of Hopf type weak solutions to the Navier-Stokes equations for arbitrary domains. Further we explain a new existence result for nonhomogeneous data and a result for global regular solutions with "slightly" modified forces.
[ 参考URL ]The aim of this talk is to explain some new results in particular on local regularity properties of Hopf type weak solutions to the Navier-Stokes equations for arbitrary domains. Further we explain a new existence result for nonhomogeneous data and a result for global regular solutions with "slightly" modified forces.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004年10月13日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 128号室
Philippe G. LeFloch 氏 (University of Paris 6)
Existence, uniqueness, and continuous dependence of entropy solutions to hyperbolic systems
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Philippe G. LeFloch 氏 (University of Paris 6)
Existence, uniqueness, and continuous dependence of entropy solutions to hyperbolic systems
[ 講演概要 ]
I will review the well-posedness theory of nonlinear hyperbolic systems, in conservative or in non-conservative form, by focusing attention on the existence and properties of entropy solutions with sufficiently small total variation.
New results and perspectives on the following issues will be discussed: Glimm's existence theorem,
Bressan-LeFloch's uniqueness theorem,and the L1 continuous dependence property (established by Bressan, LeFloch, Liu, and Yang).
[ 参考URL ]I will review the well-posedness theory of nonlinear hyperbolic systems, in conservative or in non-conservative form, by focusing attention on the existence and properties of entropy solutions with sufficiently small total variation.
New results and perspectives on the following issues will be discussed: Glimm's existence theorem,
Bressan-LeFloch's uniqueness theorem,and the L1 continuous dependence property (established by Bressan, LeFloch, Liu, and Yang).
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004年09月29日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 117号室
Alex Mahalov 氏 (Arizona State University)
Global Regularity of the 3D Navier-Stokes with Uniformly Large Initial Vorticity
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Alex Mahalov 氏 (Arizona State University)
Global Regularity of the 3D Navier-Stokes with Uniformly Large Initial Vorticity
[ 講演概要 ]
We prove existence on infinite time intervals of regular solutions to the 3D Navier-Stokes Equations for fully three-dimensional initial data characterized by uniformly large vorticity with periodic boundary conditions and in bounded cylindrical domains; smoothness assumptions for initial data are the same as in local existence theorems. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to any 2D manifold.
The global existence is proven using techniques of fast singular oscillating limits and the Littlewood-Paley dyadic decomposition. The approach is based on the computation of singular limits of rapidly oscillating operators and cancellation of oscillations in the nonlinear interactions for the vorticity field. With nonlinear averaging methods in the context of almost periodic functions, we obtain fully 3D limit resonant Navier-Stokes equations. Using Lemmas on restricted convolutions, we establish the global regularity of the latter without any restriction on the size of 3D initial data.
With strong convergence theorems, we bootstrap this into the global regularity of the 3D Navier-Stokes Equations with uniformly large initial vorticity.
[ 参考URL ]We prove existence on infinite time intervals of regular solutions to the 3D Navier-Stokes Equations for fully three-dimensional initial data characterized by uniformly large vorticity with periodic boundary conditions and in bounded cylindrical domains; smoothness assumptions for initial data are the same as in local existence theorems. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to any 2D manifold.
The global existence is proven using techniques of fast singular oscillating limits and the Littlewood-Paley dyadic decomposition. The approach is based on the computation of singular limits of rapidly oscillating operators and cancellation of oscillations in the nonlinear interactions for the vorticity field. With nonlinear averaging methods in the context of almost periodic functions, we obtain fully 3D limit resonant Navier-Stokes equations. Using Lemmas on restricted convolutions, we establish the global regularity of the latter without any restriction on the size of 3D initial data.
With strong convergence theorems, we bootstrap this into the global regularity of the 3D Navier-Stokes Equations with uniformly large initial vorticity.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004年07月05日(月)
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
https://www.ms.u-tokyo.ac.jp/gcoe/index.html
who 氏 (where)
what (JAPANESE)
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
https://www.ms.u-tokyo.ac.jp/gcoe/index.html
who 氏 (where)
what (JAPANESE)
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