2022年度のセミナーの記録
- 4 月 15 日
- 加藤 勲 氏 （京都大学） Isao Kato (Kyoto University)
- 4 月 22 日
- 勝呂 剛志 氏 （京都大学） Takeshi Suguro (Kyoto University)
- 5 月 10 日
- 戍亥 隆恭 氏 （大阪大学 / ブリティッシュコロンビア大学） Takahisa Inui (Osaka University / The University of British Columbia)
- 5 月 20 日
- Ruobing Bai 氏 （天津大学） Ruobing Bai (Tianjin University)
- 5 月 27 日
- 久藤 衡介 氏 （早稲田大学） Kousuke Kuto (Waseda University)
- 6 月 3 日
- 中村 誠 氏 （大阪大学） Makoto Nakamura (Osaka University)
- 6 月 10 日
- 溝口 紀子 氏 （東京学芸大学） Noriko Mizoguchi (Tokyo Gakugei University)
- 6 月 17 日
- 森 龍之介 氏 （明治大学） Ryunosuke Mori (Meiji University)
- 6 月 24 日
- 米田 昌史 氏 （千葉大学） Masafumi Yoneda (Chiba University)
- 7 月 1 日
- 榊原 航也 氏 （岡山理科大学 / 理化学研究所） Koya Sakakibara (Okayama University of Science / RIKEN)
- 7 月 8 日
- Katerina Nik 氏 （University of Vienna）
- 7 月 15 日
- 橋本 伊都子 氏 （金沢大学 / 大阪公立大学数学研究所） Itsuko Hashimoto (Kanazawa University / OCAMI)
- 7 月 22 日
- Neal Bez 氏 （埼玉大学） Neal Bez (Saitama University)
- 10 月 7 日
- 高田 了 氏 （東京大学） Ryo Takada (the University of Tokyo)
- 10 月 14 日
- 澤野 嘉宏 氏 （中央大学） Yoshihiro Sawano (Chuo University)
- 10 月 21 日
- 佐藤 拓也 氏 （東北大学） Takuya Sato (Tohoku University)
- 10 月 28 日
- 水野 将司 氏 （日本大学） Masashi Mizuno (Nihon University)
- 11 月 4 日
- 中村 昌平 氏 （大阪大学・バーミンガム大学） Shohei Nakamura (Osaka University / University of Birmingham)
- 11 月 11 日
- 下條 昌彦 氏 （東京都立大学） Masahiko Shimojo (Tokyo Metropolitan University)
- 11 月 18 日
- 物部 治徳 氏 （大阪公立大学） Harunori Monobe (Osaka Metropolitan University)
- 11 月 25 日
- 柳 青 氏 （沖縄科学技術大学院大学） Qing Liu (OIST, Okinawa Institute of Science and Technology Graduate University)
- 12 月 2 日
- Guopeng Li 氏 （Maxwell Institute for Mathematical Sciences）
Tadahiro Oh 氏 （The University of Edinburgh） - 12 月 9 日
- 鈴木 聡一郎 氏 （名古屋大学） Soichiro Suzuki (Nagoya University)
- 12 月 16 日
- 宋 自昊 氏 （南京航空航天大学・京都大学） Zihao Song (Nanjing University of Aeronautics and Astronautics / Kyoto University)
- 1 月 6 日
- Ming Mei 氏 （McGill University / Champlain College St-Lambert, Canada）
- 1 月 13 日
- 清水 一慶 氏 （大阪大学） Ikkei Shimizu (Osaka University)
- 1 月 20 日
- 加藤 孝盛 氏 （佐賀大学） Takamori Kato (Saga University)
- 1 月 27 日
- 青木 基記 氏 （東北大学） Motofumi Aoki (Tohoku University)
- 講演者
- 加藤 勲 氏 （京都大学理学研究科）
Isao Kato (Department of Mathematics, Graduate School of Science, Kyoto University) - 講演題目
- A remark on the ill-posedness for the half wave Schrödinger equations
- 講演要旨
- 本講演では，half wave Schrödinger 方程式の初期値問題を考える． Xu (2017) により斥力的 3 次非線型項かつシリンダー上で解の漸近挙動が考察されたのを機に，Bahri-Ibrahim-Kikuchi (2021) により非線型項が集約的かつ小さな冪指数の場合の定在波解の存在や安定性などが示された． また初期値問題の適切性に関してエネルギー劣臨界空間での時間局所適切性が示されているが，非適切性に関する結果は知られていない． そこで本講演では，Christ-Colliander-Tao (2003) の方法に基づき，尺度優臨界空間における非適切性を述べる． また，集約的で冪指数が小さいときの尺度臨界空間での非適切性についても言及する． なお，時間が許せばエネルギー臨界空間における適切性及び尺度劣臨界空間における非適切性に関する注意も述べたい．
- 講演者
- 勝呂 剛志 氏 （京都大学数理解析研究所）
Takeshi Suguro (Research Institute for Mathematical Sciences, Kyoto University) - 講演題目
- 一様局所可積分空間における Keller--Segel 系の特異極限問題について
Singular limit problem for the Keller--Segel system in uniformly local spaces - 講演要旨
- 本講演では，一様局所可積分空間における Keller--Segel 系の初期値問題を考える． この方程式系は非線形項に非局所的な移流効果を擁するため，遠方において減衰しない函数を取り扱う一様局所可積分空間において初期値問題の適切性の検証は一般的に困難である． ここでは，一様局所可積分空間における Keller--Segel 系の初期値問題の適切性を示し，放物-楕円型 Keller--Segel 系を導く緩和時間零極限を考察する． 特異極限問題の証明においては，非回帰的である一様局所可積分空間の実補間空間における熱方程式の初期値問題の解に対する最大正則性理論を適用する． なお，本講演は，小川卓克氏（東北大学）との共同研究に基づく．
- 講演者
- 戍亥 隆恭 氏 （大阪大学 / ブリティッシュコロンビア大学）
Takahisa Inui (Osaka University / The University of British Columbia) - 講演題目
- 1 次元空間上の非線形シュレディンガー方程式に対する，閾値における奇関数解の時間挙動について
Threshold odd solutions to the nonlinear Schrödinger equation in one dimension - 講演要旨
- 本講演では，1 次元ユークリッド空間における非線形シュレディンガー方程式の奇関数解を考える． 奇関数解においては，基底状態解のアクションの 2 倍よりも真に小さいアクションを持つ解は，散乱するか爆発するかのいずれかであることが知られている． ここでは，基底状態解のアクションの 2 倍と同じアクションを持つ奇関数解も散乱するか爆発するかのいずれかであることを示す． 本研究は，日本学術振興会の海外特別研究員制度の支援の下で行った，Stephen Gustafson 教授（ブリティッシュコロンビア大学）との共同研究である．
- 講演者
- Ruobing Bai 氏 （Center for Applied Mathematics, Tianjin University）
- 講演題目
- Large global solutions for energy-critical nonlinear Schrödinger equation
- 講演要旨
- こちら
- 講演者
- 久藤 衡介 氏 （早稲田大学）
Kousuke Kuto (Waseda University) - 講演題目
- 重定-川崎-寺本モデルの定常解の交差拡散極限
Cross-diffusion limit of steady-state solutions to the Shigesada-Kawasaki-Teramoto model - 講演要旨
- 交差拡散とよばれる非線形拡散項を伴うロトカ・ボルテラ系は，競争種の棲み分けの数理モデルとして重定，川崎，寺本 (1979) によって提唱されている． 本講演においては，両方の種の交差拡散係数を無限大にしたときの定常解の漸近挙動を考察する． 前半部では，定常解のアプリオリ評価を，両方の交差拡散係数に依存しない形で導出し，漸近挙動が唯一の極限系の解で特徴付けられることを示す． 後半部では，とくに空間 1 次元において極限系の解集合の大域分岐構造を示す．
- 講演者
- 中村 誠 氏 （大阪大学大学院情報科学研究科）
Makoto Nakamura (Graduate School of Information Science and Technology, Osaka University) - 講演題目
- Global solutions for semilinear Proca equations in the de Sitter spacetime
- 講演要旨
- The Cauchy problem for the semilinear Proca equations is considered in the de Sitter spacetime. Several effects of the spatial expansion on the existence of solutions of the equations are considered. Global solutions for small data are shown based on the dissipative effect caused by the spatial expansion.
- 講演者
- 溝口 紀子 氏 （東京学芸大学）
Noriko Mizoguchi (Tokyo Gakugei University) - 講演題目
- Complete classification of gradient blow-up and recovery of boundary condition for the viscous Hamilton-Jacobi equation
- 講演要旨
- In this talk, I give a complete classification of GBU (gradient blowup) and RBC (recovery of boundary condition) to general solutions of viscous Hamilton Jacobi equation in one space dimension. Namely, I determine the profile including precise rate with its stability/instability.
- 講演者
- 森 龍之介 氏 （明治大学）
Ryunosuke Mori (Meiji University) - 講演題目
- 移流項付き一般化平均曲率流の正則性
Regularity of solutions to generalized mean curvature flow with transport term - 講演要旨
-
Suppose that a family of k-dimensional surfaces in R^n evolves by the generalized mean curvature flow
with a given transport vector in the sense of Brakke's formulation of velocity.
When the flow is locally close to a time-dependent k-dimensional plane in a weak sense of measure in space-time,
it is represented as a graph of a C^{1,α} function over the plane.
On the other hand, it is not known if the graph satisfies the corresponding PDE pointwise in general.
For this problem, when k=n-1 and the distributional time derivative of the graph is a signed Radon measure, it is proved that the graph satisfies the PDE pointwise. This talk is based on a joint work [arXiv:2109.06380] with Professor Yoshihiro Tonegawa (Tokyo Tech) and Eita Tomimatsu (Tokyo Tech).
- 講演者
- 米田 昌史 氏 （千葉大学大学院融合理工学府）
Masafumi Yoneda (Graduate School of Science and Engineering, Chiba University) - 講演題目
- Asymptotic stability of soliton for discrete nonlinear Schrödinger equation on one-dimensional lattice
- 講演要旨
- In this talk we consider the discrete Schrödinger equation on 1D lattice. In particular, we prove the asymptotic stability of soliton near anti-continuous limit. We prove the theorem by using Strichartz estimate for discrete Laplacian with Dirichlet condition on the origin, which is almost like a free discrete Laplacian restricted on odd functions.
- 講演者
- 榊原 航也 氏 （岡山理科大学 / 理化学研究所）
Koya Sakakibara (Okayama University of Science / RIKEN) - 講演題目
- 悪条件性を緩和した基本解近似解法の数学解析
Mathematical analysis of the well-conditioned method of fundamental solutions - 講演要旨
- 基本解近似解法（MFS）とは，線型偏微分方程式に対するメッシュフリー数値解法であり，特に工学などの応用分野で広く用いられている． しかしながら，豊富な応用研究の一方で数学解析の結果は非常に少なく，また，選点法から得られる選点方程式は悪条件となるなど，数理的に考えるべき課題がまだまだ残されている． 本講演では，MFS の数学解析の研究の歴史を概観した後，近年提案された，悪条件性を克服した定式化である MFS-QR 法の数学解析の結果について報告する．
- 講演者
- Katerina Nik 氏 （Faculty of Mathematics, University of Vienna）
- 講演題目
- On a three-dimensional model for MEMS with a hinged upper plate
- 講演要旨
-
An idealized electrostatic microelectromechanical system (MEMS)
consists of a rigid ground plate above which a thin elastic plate is suspended.
The elastic plate is assumed to be hinged on its boundary.
Applying a voltage difference between the two plates induces a Coulomb force that deforms the elastic plate.
The corresponding mathematical model couples a fourth-order parabolic equation for the vertical deformation of the elastic plate
to the harmonic electrostatic potential in the free domain between the two plates.
In this talk, I will present some recent results on local and global well-posedness of the model as well as on existence and non-existence of stationary solutions.
- 講演者
- 橋本 伊都子 氏 （金沢大学機械工学系 / 大阪公立大学数学研究所）
Itsuko Hashimoto (School of Mechanical Engineering, Kanazawa univercity / OCAMI) - 講演題目
- Asymptotic behavior toward radially symmetric stationary solutions of the compressible Navier-Stokes equation
- 講演要旨
- This talk is concerned with the asymptotic behaviors of radially symmetric stationary solutions for the compressible Navier-Stokes equation. We discuss the motion of viscous barotropic gas without external forces, where boundary and far field data are prescribed on the exterior domain. For both inflow and outflow problems, the asymptotic behaviors of radially symmetric stationary solutions is shown in a suitably small neighborhood of the initial data. This research is the joint work with Professor Nishibata and Sugizaki of Tokyo Institute of technology and Matsumura of Osaka university.
- 講演者
- Neal Bez 氏 （埼玉大学）
Neal Bez (Saitama University) - 講演題目
- Stability of the hypercontractivity inequality
- 講演要旨
- Nelson's gaussian hypercontractivity inequality captures the regularising property of the Ornstein--Uhlenbeck semigroup. Although early motivation arose from quantum field theory, the hypercontractivity inequality is wide-reaching and enjoys connections to a variety of topics. In this talk, we discuss a refinement of the hypercontractivity inequality when the class of input functions is restricted. Making contact with recent work of Eldan, Lehec and Shenfeld, we will derive certain deficit estimates for the log-Sobolev inequality from our refined version of hypercontractivity. This talk is based on joint work with Shohei Nakamura and Hiroshi Tsuji (both at Osaka).
- 講演者
- 高田 了 氏 （東京大学大学院数理科学研究科）
Ryo Takada (Graduate School of Mathematical Sciences, the University of Tokyo) - 講演題目
- Global solutions for the incompressible rotating MHD equations in the scaling critical Sobolev space
- 講演要旨
- We consider the initial value problem for the incompressible MHD equations with the Coriolis force in the 3D whole space. We prove the global in time existence and the uniqueness of solutions for large initial data in the scaling critical Sobolev space when the speed of rotation is sufficiently high. In order to control the large magnetic fields, we introduce a modified linear solution for the velocity, and show its smallness in a suitable space-time norm by means of the dispersive effect of the Coriolis force.
- 講演者
- 澤野 嘉宏 氏 （中央大学理工学部数学科）
Yoshihiro Sawano (Department of Mathematics, Faculty of Science and Engineering, Chuo University) - 講演題目
- Harmonic analysis and maximal regularity
- 講演要旨
-
The goal of this talk is to prove the existence for the Keller-Segel equation with the initial data in Besov-Morrey spaces.
A closer inspection shows that the maximal regularity has a lot to do with the local means in the theory of function spaces.
It is well known that the second integrability index of Besov spaces plays an important role to compare the property of functions. This fact will be included in our theorem in maximal regularity.
This is a joint work with Toru Nogayama at Chuo University.
- 講演者
- 佐藤 拓也 氏 （東北大学大学院理学研究科）
Takuya Sato (Graduate School of Science, Tohoku University) - 講演題目
- On the mass decay of solutions to dissipative nonlinear Schrödinger equations
- 講演要旨
- 非線形消散効果を備える非線形 Schrödinger 方程式について，解の二乗可積分ノルム（質量）の減衰・非減衰といった時間大域挙動が，非線形項の指数に応じて分類できることが知られている． ここでは，非線形項が臨界次数を持つ場合に，解の質量は減衰し，その減衰オーダーが解の空間変数の正則性に依存することを示す． また，最適な質量減衰を示す特別な解の存在についても述べる．
- 講演者
- 水野 将司 氏 （日本大学理工学部数学科）
Masashi Mizuno (Department of Mathematics, College of Science and Technology, Nihon University) - 講演題目
- Long-time asymptotic behavior for a non-linear Fokker-Planck model with spatial inhomogeneous free energy
- 講演要旨
- The conservation law of mass, also called the continuity equation, is a fundamental law in physics. In this talk, first, we derive the velocity in order to guarantee energy dissipation for given free energy with the spatial inhomogeneous absolute temperature along with the conservation law. The spatial inhomogeneous absolute temperature yields nonlinearity, in contrast with the homogeneous case. As a result, the conservation law turns into a non-linear Fokker-Planck model. Next, we study mathematical analysis, especially long-time asymptotics of the model. This analysis is based on so-called entropy dissipation methods for the linear Fokker-Planck equation. If time permits, we will explain the connection to the grain boundary motion.
- 講演者
- 中村 昌平 氏 （大阪大学理学研究科・バーミンガム大学）
Shohei Nakamura (Graduate School of Science, Osaka University / University of Birmingham) - 講演題目
- Local well-posedness of the periodic Zakharov system with low regularity via decoupling theory
- 講演要旨
- This talk is based on a joint work with Shinya Kinoshita (Saitama) and Akansha Sanwal (Bielefeld). Our purpose is to establish the local well-posedness of the periodic Zakharov system with low regularity on torus $\mathbb{T}^d$ with $d\ge3$. The sharp regularity ensuring the local well-posedness is known for $d=1$ due to Takaoka and $d=2$ due to Kishimoto while the problem for $d\ge3$ is open despite of the progress by Kishimoto. We attack to this problem by introducing recent developments of so-called decoupling inequality (Wolff’s inequality) from Fourier restriction theory and improve Kishimoto’s local well-posedness result for $d\ge3$. At the same time, the study of the periodic Zakharov system raises a question on some trilinear estimates involving free solutions of Schrödinger and wave equations on torus which can be regarded as some trilinear decoupling type estimates involving paraboloid and cone.
- 講演者
- 下條 昌彦 氏 （東京都立大学理学部数理学科）
Masahiko Shimojo (Department of Mathematical Sciences, Faculty of Science, Tokyo Metropolitan University) - 講演題目
- Spreading phenomena of reaction-diffusion systems and Liouville-type theorem
- 講演要旨
- The aim of this talk is to study the asymptotic behavior of solutions for some reaction-diffusion systems. By an entire solution, we mean a solution of the reaction-diffusion system which is guaranteed to exist for all real-time in the whole Euclidean space. We establish a Liouville-type theorem for the entire solutions of reaction-diffusion systems. Several examples of spreading phenomena from ecology and epidemiology are given to illustrate the applications of this theory.
- 講演者
- 物部 治徳 氏 （大阪公立大学大学院理学研究科）
Harunori Monobe (Graduate School of Science, Osaka Metropolitan University) - 講演題目
- Compact traveling waves for anisotropic mean-curvature flow with driving force
- 講演要旨
-
Mean-curvature flow with a driving force appears in various mathematical problems such as motion of soap films, grain boundaries and singular limit problems of various reaction diffusion systems, e.g., FitzHugh-Nagumo equation.
In this talk, we show the existence and uniqueness of traveling waves, composed of a Jordan curve (or closed surface), for an anisotropic curvature flow with a driving force. We call such a solution "compact traveling wave" in this talk. Our aim is to investigate the condition of external driving force when the curvature flow has traveling waves.
- 講演者
- 柳 青 氏 （沖縄科学技術大学院大学）
Qing Liu (OIST, Okinawa Institute of Science and Technology Graduate University) - 講演題目
- Principal eigenvalue problem for infinity Laplacian in metric spaces
- 講演要旨
-
This talk is concerned with the Dirichlet eigenvalue problem associated to the infinity Laplacian in metric spaces.
We provide a direct PDE approach to find the principal eigenvalue and eigenfunctions for a bounded domain in a proper geodesic space with no measure structure.
We give an appropriate notion of solutions to the infinity eigenvalue problem and show the existence of solutions by adapting Perron's method.
Our method is different from the standard limit process, introduced by Juutinen, Lindqvist and Manfredi in 1999, via the variational eigenvalue formulation for p-Laplacian in the Euclidean space.
This talk is based on joint work with Ayato Mitsuishi at Fukuoka University.
【Talk I】(16:00 〜 16:40)
- 講演者
- Guopeng Li 氏 （Maxwell Institute for Mathematical Sciences）
- 講演題目
- Deep-water and shallow-water limits of the intermediate long wave equation: from deterministic and statistical viewpoints
- 講演要旨
-
In this talk, I will discuss the convergence problem for the intermediate long wave equation (ILW) from deterministic and statistical viewpoints.
ILW models the internal wave propagation of the interface in two-layer fluid of finite depth,
providing a natural connection between the Korteweg-de Vries equation (KdV) in the shallow-water limit and the Benjamin-Ono equation (BO) in the deep-water limit.
In the first part of this talk, I discuss the convergence problem for ILW in the low regularity setting from a deterministic viewpoint. In particular, by establishing a uniform (in depth) a priori bound, I show that a solution to ILW converges to that to KdV (and to BO) in the shallow-water limit (and in the deep-water limit, respectively).
In the second part of this talk, I discuss an analogous convergence result from a statistical viewpoint. More precisely, I study convergence of invariant Gibbs dynamics for ILW in the shallow-water and deep-water limits. After a brief review on the construction of the Gibbs measure for ILW, I show that the Gibbs measures for ILW converge in total variation to that for BO in the deep-water limit, while in the shallow-water limit, we can only show weak convergence of corresponding Gibbs measures for ILW to that for KdV. In terms of dynamics, we use a compactness argument to construct invariant Gibbs dynamics for ILW (without uniqueness) and show that they converge to invariant Gibbs dynamics for KdV and BO in the shallow-water and deep-water limits, respectively.
The second part of the talk is based on joint work with Tadahiro Oh (The University of Edinburgh) and Guangqu Zheng (University of Liverpool).
【Talk II】(16:50 〜 17:30)
- 講演者
- Tadahiro Oh 氏 （The University of Edinburgh）
- 講演題目
- Hyperbolic P(\Phi)_2 model on the plane
- 講演要旨
-
I will discuss well-posedness of the stochastic damped nonlinear wave equation (SdNLW) forced by a space-time white noise with the Gibbsian initial data.
This problem is also known as the hyperbolic $\Phi^{k+1}_2$-model since it corresponds to the so-called canonical stochastic quantization of the $\Phi^{k+1}_2$-measure.
In this talk, our main goal is to study this problem on the plane.
Previously, this problem was studied on the two-dimensional torus by Gubinelli-Koch-Oh-Tolomeo (2021). By introducing a proper renormalization, they constructed global-in-time invariant Gibbs dynamics. By taking a large torus limit, I aim to construct invariant Gibbs dynamics for the hyperbolic $\Phi^{k+1}_2$-model on the plane.
First, I plan to go over the construction of a $\Phi^{k+1}_2$-measure on the plane as a limit of the $\Phi^{k+1}_2$-measures on large tori. This is done by establishing coming-down-from-infinity for the associated stochastic nonlinear heat equation (SNLH) on the plane. We then construct invariant Gibbs dynamics for the hyperbolic $\Phi^{k+1}_2$-model on the plane by taking a limit of the invariant Gibbs dynamics on large tori. Our strategy is inspired by a recent work by Oh-Okamoto-Tolomeo (2021) on the hyperbolic $\Phi^3_3$-model on the three-dimensional torus, where we reduce the problem to studying convergence of the so-called extended Gibbs measures. By combining wave and heat analysis together with ideas from optimal transport theory, I establish convergence of the extended Gibbs measures.
- 講演者
- 鈴木 聡一郎 氏 （名古屋大学大学院多元数理科学研究科）
Soichiro Suzuki (Graduate School of Mathematics, Nagoya University) - 講演題目
- Energy decay estimates of the fractional Klein--Gordon equation with space-dependent damping
- 講演要旨
- We consider the fractional Klein--Gordon equation on $\mathbb{R}^d$ with space-dependent damping. Our main aim is to establish the equivalence between energy decay estimates of the equation and a kind of the uncertainty principle in Fourier analysis. In addition, we give a new sufficient condition for the polynomial decay using the equivalence. This is a joint work with Kotaro Inami (Nagoya University).
- 講演者
- 宋 自昊 氏 （南京航空航天大学・京都大学数理解析研究所）
Zihao Song (Nanjing University of Aeronautics and Astronautics / RIMS, Kyoto University) - 講演題目
- Global dynamics of L^p solutions to the compressible Korteweg system
- 講演要旨
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In this talk, we shall concern with the Cauchy problem of the viscous compressible fluids of Korteweg type in zero sound speed case.
It is found that the linearized system admits the purely parabolic structure where acoustic waves are not available in our models,
which enables us to establish the global-in-time existence and Gevrey analyticity of strong solutions in hybrid Besov spaces of $L^p$-type for $d\geq3$.
We also present a new derivation for the optimal decay of arbitrary higher order derivatives for $L^p$ solutions. This approach, based on Gevrey analyticity we established, reduces the decay problem to establishing uniform bounds on the growth of the radius of analyticity for the solution under a negative regularity. Compared to the classical time-weight energy method, this approach concerns only a regularity problem allowing us to get asymptotic behaviors without asking smallness condition for the initial assumption and is applicable to a wide range of dissipative systems.
This talk is based on joint works with professor Jiang Xu at Nanjing University of Aeronautics and Astronautics.
- 講演者
- Ming Mei 氏 （McGill University / Champlain College St-Lambert, Canada）
- 講演題目
- Subsonic/supersonic/transonic steady-states of Euler-Poisson equations for semiconductors with sonic boundary
- 講演要旨
- In this talk, we mainly investigate and classify the existence/non-existence, uniqueness/multipleness, regularity/singularity of the physical solutions such as subsonic/supersonic/transonic steady-states of Euler-Poisson equations for semiconductors with sonic boundary. The sonic boundary, a critical case, usually makes the structure of solutions to be various and fantastic, and causes some singularities for the solutions.
- 講演者
- 清水 一慶 氏 （大阪大学大学院基礎工学研究科）
Ikkei Shimizu (Graduate School of Engineering Science, Osaka University) - 講演題目
- Phase transition threshold and stability of magnetic skyrmions
- 講演要旨
- We consider the minimization problem of the Landau-Lifshitz energy with the Dzyaloshinskii-Moriya interaction term, including its coefficient as a parameter. This functional admits an explicit critical point with the vortex-type configuration, called (magnetic) skyrmion in physical context. In this talk, we show that there exists an explicit critical value of the parameter above which the skyrmion is unstable, while stable below this threshold. This is a mathematical result consistent with some experiments and numerical studies. This talk is based on the joint work [arXiv:2210.00892] with Slim Ibrahim (UVic).
- 講演者
- 加藤 孝盛 氏 （佐賀大学理工学部）
Takamori Kato (Faculty of Science and Engineering, Saga University) - 講演題目
- 周期境界条件下での 5 次 KdV 型方程式に対する適切性と無条件一意性
Unconditional well-posedness for fifth order KdV type equations on the torus - 講演要旨
- 本講演では，周期境界条件下での 5 次 KdV 型方程式に対する初期値問題の適切性を考察する． この方程式は，KdV 階層に属する 5 次 KdV 方程式を一般化した非線形分散型方程式であり，非線形項が持つ 3 階の微分をどのように処理するかが鍵となる． 特に，方程式を線形化方程式の解の周りで展開した際に，微分の損失を持つ共鳴部分が高次の項に現れることが問題となるが，方程式の対称性，特に保存量と変数変換を用いることで，この共鳴部分を相殺することが可能になる． また非共鳴部分には normal form 法を適用することで，平滑化効果を引き出すことができ，超関数の意味で解が定義できる臨界の指数での適切性と無条件一意性が得られることを述べる． なお，本講演は津川光太郎氏（中央大学）との共同研究の内容に基づく．
- 講演者
- 青木 基記 氏 （東北大学大学院理学研究科）
Motofumi Aoki (Graduate School of Science, Tohoku University) - 講演題目
- On sufficient conditions of the energy conservation law for the full system of compressible Navier-Stokes equations
- 講演要旨
- 本講演では，空間 2 次元および 3 次元における圧縮性ナヴィエ・ストークス方程式のエネルギー保存則について考える． 方程式は質量の式，運動方程式，内部エネルギーの式から構成される方程式を扱う． 弱解の存在は Feireisl(2004) によって示されており，本講演では，密度関数と速度場が一定の条件を満たすとき，全エネルギーが保存することを示す． また，主題であるエネルギー保存のための数理的条件と温度付き圧縮性ナヴィエ・ストークス方程式の初期値問題の非適切性との関連についても述べる． 本講演は，岩渕司氏（東北大学）との共同研究に基づく．