Applied Analysis

Seminar information archive ~09/27Next seminarFuture seminars 09/28~

Date, time & place Thursday 16:00 - 17:30 002Room #002 (Graduate School of Math. Sci. Bldg.)

Seminar information archive


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
東海林 まゆみ (日本女子大学・理学部・数物科学科)
Particle trajectories around a running cylinder in Brinkman's porous-media flow
[ Abstract ]
Motion of fluid particles provides us with interesting problems of dynamical
systems. We consider here the movement of particles around a running cylinder.
Classically J. C. Maxwell (1870) considered the problem in irrotational flow of
inviscid fluid. He showed that the complete solution is given by the elliptic
functions and the trajectory forms one of the elastica curves. C. Darwin ('53)
considered a similar problem for a moving sphere. In this case, the solution
cannot be written in terms of elliptic functions but can be expressed by a
simple definite integral.
We consider a similar problem in Brinkman's porous-media flow which is proposed
by Brinkman ('49). Our numerical examinations reveals some new interesting
features of the particle trajectories which are not observed in the case of
irrotational flow. We will report them.


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
池田 幸太 (明治大 研究・知財戦略機構)
[ Abstract ]


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Jin CHENG (程 晋) (復旦大学)
Heat transfer in composite materials with Stenfen-Boltzmann conditions and related inverse problems
[ Abstract ]
In this talk, we will present our recent results on the mathematical model of the heat transfer in the composite materials. The related inverse problems are discussed. The numerical results show our methods are effective.


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
千葉 逸人 (京都大学 情報学研究科)
Extension and Unification of Singular Perturbation Methods for ODE's Based on the Renormalization Gourp Method
[ Abstract ]
くりこみ群の方法は微分方程式に対する特異摂動法の一種であり,多重尺度法、平均化法、normal forms, 中心多様体縮約、位相縮約、WKB解析などの古くから知られる摂動法を統一的に扱うことができる.ここではくりこみ群の方法を数学的定式化を与え,結合振動子系などへのいくつかの応用も紹介したい.


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
木村 正人 (九州大学・大学院数理学研究院)
On a phase field model for mode III crack growth
[ Abstract ]


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Jan Haskovec
(Vienna University of Technology(オーストリア))
Stochastic Particle Approximation for Measure Valued Solutions of the 2D Keller-Segel System
[ Abstract ]
We construct an approximation to the measure valued, global in time solutions to the Keller-Segel model in 2D, based on systems of stochastic interacting particles. The advantage of our approach is that it reproduces the well-known dichtomy in the qualitative behavior of the system and, moreover, captures the solution even after the possible blow-up events. We present a numerical method based on this approach and show some numerical results. Moreover, we make a first step toward the convergence analysis of our scheme by proving the convergence of the stochastic particle approximation for the Keller-Segel model with a regularized interaction potential. The proof is based on a BBGKY-like approach for the corresponding particle distribution function.


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
杉山 由恵 (津田塾大学・学芸学部・数学科)
Aronson-Benilan type estimate and the optimal Hoelder continuity of weak solutions for the 1D degenerate Keller-Segel systems
[ Abstract ]
We consider the Cauchy problem for the 1D Keller-Segel system of degenerate
type (KS)_m with $m>1$:
u_t= \\partial_x^2 u^m - \\partial_x (u^{q-2} \\partial_x v),
-\\partial_x^2 v + v - u=0.
We establish a uniform estimate from below of $\\partial_x^2 u^{m-1}$.
The corresponding estimate to the porous medium equation is well-known
as an Aronson-Benilan type.
As an application of our Aronson-Benilan type estimate,
we prove the optimal Hoelder continuity of the weak solution $u$ of (KS)_m.
In addition, we find that the positive region $D(t):=\\{x \\in \\R; u(x,t)>0\\}$
of $u$ is monotonically non-decreasing with respect to the time $t$.


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Joseph F. Grotowski (University of Queensland)
Two-dimensional harmonic map heat flow versus four-dimensional Yang-Mills heat flow
[ Abstract ]
Harmonic map heat flow and Yang-Mills heat flow are the gradient flows associated to particular energy functionals. In the considered dimension, (i.e. dimension two for the harmonic map heat flow, dimension four for the Yang-Mills heat flow), the associated energy functional is (locally) conformally invariant, that is, the dimension is critical. This leads to a number of interesting phenomena when considering both the functionals and the associated flows. In this talk we discuss qualitative similarities and differences between the flows.


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
渡辺 達也 (早稲田大学・理工学術院)
Two positive solutions for an inhomogeneous scalar field equation
[ Abstract ]
We consider the following nonlinear elliptic equation:
$$-\\Delta u+u=g(u)+f(x), x \\in R^N,$$
where $N\\ge 3$. When $f(x)\\equiv 0$, it is known that there is a nontrivial solution for a wide class of nonlinearities. Even though $f(x) \\not\\equiv 0$, we can expect the existence of a nontrivial solution if $f(x)$ is small in a suitable sense. Our purpose is to show the existence of two positive solutions via the variational approach when $\\| f\\|_{L^2}$ is small. The first solution is characterized as a local minimizer. The second solution will be obtained by the Mountain Pass Method. Since we do not impose any global condition on the nonlinearity, we will need a presice interaction estimate.


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
谷口 雅治 (東京工業大学大学院情報理工学研究科)
(The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen-Cahn equations)

[ Abstract ]
We study the uniqueness and the asymptotic stability of a pyramidal traveling front in the three-dimensional whole space. For a given admissible pyramid we prove that a pyramidal traveling front is uniquely determined and that it is asymptotically stable under the condition that given perturbations decay at infinity. For this purpose we characterize the pyramidal traveling front as a combination of planar fronts on the lateral surfaces. Moreover we characterize the pyramidal traveling front in another way, that is, we write it as a combination of two-dimensional V-form waves on the edges. This characterization also uniquely determines a pyramidal traveling front.


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
齊藤 宣一 (東京大学大学院数理科学研究科)
[ Abstract ]


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
森 洋一朗 (University of British Columbia)
[ Abstract ]

電気生理学が対象とするのは細胞および組織レベルでの電気活動であり,これは神経・心・内分泌機能の根幹をなすものである.Hodgkin とHuxley の有名な仕事を契機として,この方面の研究は数理生理学に格好の題材を提供し続けてきた.本講演では,まず電気生理の基礎概念を紹介した後,イオン動態と細胞膜の3次元形状の効果を取り入れたモデルについて解説し,その心臓生理学への応用について語る.さらに時間が許せば,私が今興味を持っている細胞極性の生成,細胞の動きなどの話題についても紹介したい.


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
小磯 深幸 (奈良女子大学理学部数学教室)
( Stability and uniqueness for surfaces with constant anisotropic mean curvature)
[ Abstract ]


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
宮本 安人 (東京工業大学 大学院理工学研究科)
[ Abstract ]
円盤領域(2次元球領域)におけるNeumann問題 Δu+\\lambda f(u)=0 を考える.広いクラスの非線形項 f に対して,第2固有値と第3固有値から非球対称解からなる大域的な枝(シート)が分岐することを示し,第2固有値からの分岐の枝は,分岐直後は一意的であることを示す.


16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
WEISS Georg (東京大学大学院数理科学研究科)
Hidden dynamics and pulsating waves in self-propagating high temperature synthesis
[ Abstract ]
We derive the precise limit of SHS in the high activation energy scaling suggested by B.J. Matkowksy-G.I. Sivashinsky in 1978 and by A. Bayliss-B.J. Matkowksy-A.P. Aldushin in 2002. In the time-increasing case the limit coincides with the Stefan problem for supercooled water with spatially inhomogeneous coefficients. In general it is a nonlinear forward-backward parabolic equation with discontinuous hysteresis term.

In the first part we give a complete characterization of the limit problem in the case of one space dimension. In the second part we construct in any finite dimension a rather large family of pulsating waves for the limit problem. In the third part, we prove that for constant coefficients the limit problem in any finite dimension does not admit non-trivial pulsating waves.
This is a joint work with Regis MONNEAU (CERMICS, France).


16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Radu IGNAT (パリ南大学(オルセー))
A compactness result in micromagnetics
[ Abstract ]
We study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem, depending on two parameters, for maps with values into the unit sphere. There is a physical prediction for the optimal configuration of the magnetization called the Landau state. Our goal is to prove compactness of the Landau state. This is a joint work with Felix Otto.


16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Danielle Hilhorst (CNRS / パリ第11大学)
Singular limit of a competition-diffusion system
[ Abstract ]
We revisit a competition-diffusion system for the densities of biological populations, and (i) prove the strong convergence in L^2 of the densities of the biological species (joint work with Iida, Mimura and Ninomiya); (ii) derive the singular limit of some reaction terms as the reaction coefficient tends to infinity (joint work with Martin and Mimura).


16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
柳田 英二 (東北大学大学院理学研究科)
[ Abstract ]
この講演では,藤田型の半線形放物型偏微分方程式に関する M. Fila, J. King, P. Polacik, M. Winkler らとの共同研究による成果についてその概要を紹介する.全空間上の藤田型方程式については,これまで様々な挙動を示す時間大域解の存在が示されている.そこで大域解の時間的挙動と初期値の空間的挙動の関係を詳細に調べることにより,大域解をいくつかに分類し,その挙動がそれぞれ異なるメカニズムに支配されていることを明らかにする.時間が許せば,最近の進展や関連する話題についても触れる予定である.


16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
佐藤 洋平 (早稲田大学・基幹理工学部・数学科)
Critical frequencyをもつ非線形シュレディンガー方程式のマルチピーク解
[ Abstract ]
$$ -\\epsilon2 \\Delta u +V(x)u= u^p, u>0 \\ \\hbox{in} \\R^N,
u\\in H1(\\R^N)$$
において、$\\epsilon \\to 0$ としたときに V(x) の k個の極小点にピークが集中していくマルチピーク解 $u_\\epsilon$ について考える。
ここで、p はsuperlinear, subcriticalの条件を満たし, ポテンシャル関数 V(x) は非負の有界な関数で $\\liminf_{|x|\\to \\infty}V(x)>0$ を満たすとする。

もし V(x) の各極小点に集中するピークがあるとしたら、そのピークの形状や大きさはその極小値が正であるか、0であるかによって大きく異なることが知られている。
この講演では V(x) の各極小値が正であるか 0 であるかにかかわらず、各 k個の極小点にピークが集中するマルチピーク解 $u_\\epsilon$ を構成する。


16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
倉田 和浩 (首都大学東京・理工学研究科・数理情報科学専攻)
弱い飽和効果をもったGierer-Meinhardt systemにおける軸対称領域上での多重ピーク解の構成と漸近挙動について
[ Abstract ]
This talk is based on the joint work with Kotaro Morimoto (Tokyo Metropolitan University).

We are concerned with stationary solutions to the following reaction diffusion system which is called the Gierer-Meinhardt system with saturation.
$A_t=\\epsilon^2 \\Delta A-A+A^2/(H(1+kA^2), A>0,$
$\\tau H_t=D\\Delta H-H+A2, H>0,$
where $\\epsilon >0$, $\\tau \\geq 0$, $k>0$.
The unknowns $A$ and $H$ represent the concentrations of the activator and the inhibitor. Here $\\Omega$ is a bounded smooth domain in $R^N$ and we consider homogeneous Neumann boundary conditions. When $\\Omega$ is an $x_N$-axially symmetric domain and $2\\leq N\\leq 5$, for sufficiently small $\\epsilon>0$ and large $D>0$, we construct a multi-peak stationary solution peaked at arbitrarily chosen intersections of $x^N$-axis and $\\partial \\Omega$, under the condition that $k\\epsilon^{-2N}$ converges to some $k_0\\in[0,\\infty)$ as $\\epsilon \\to 0$.

In my talk, I will explain related results comparing the differences between the case $k=0$ and $k>0$, the basic strategy of the proof of our results with some details, and open questions.


16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Robert P. GILBERT (デラウェア大学・数学教室)
Acoustic Modeling and Osteoporotic Evaluation of Bone
[ Abstract ]
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.


15:00-16:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Ratnasingham SHIVAJI (ミシシッピ州立大学)
Multiple positive solutions for classes of elliptic systems with combined nonlinear effects
[ Abstract ]
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.


16:00-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Michael TRIBELSKY (東大・数理 / モスクワ工科大学)
Soft-mode turbulence as a new type of spatiotemporal chaos at onset


16:00-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
LIANG Xing (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
[ Abstract ]
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


16:00-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Susan Friedlander (University of Illinois-Chicago)
An Inviscid Dyadic Model For Turbulence
[ Abstract ]
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.

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