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GCOE Seminars
Seminar information archive ～04/23｜Next seminar｜Future seminars 04/24～
Seminar information archive
2010/12/03
11:00-12:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Jarmo Hietarinta (University of Turku)
Discrete Integrability and Consistency-Around-the-Cube (CAC) (ENGLISH)
Jarmo Hietarinta (University of Turku)
Discrete Integrability and Consistency-Around-the-Cube (CAC) (ENGLISH)
[ Abstract ]
For integrable lattice equations we can still apply many integrability criteria that are regularly used for continuous systems, but there are also some that are specific for discrete systems. One particularly successful discrete integrability criterion is the multidimensional consistency, or CAC. We review the classic results of Nijhoff and of Adler-Bobenko-Suris and then present some extensions.
For integrable lattice equations we can still apply many integrability criteria that are regularly used for continuous systems, but there are also some that are specific for discrete systems. One particularly successful discrete integrability criterion is the multidimensional consistency, or CAC. We review the classic results of Nijhoff and of Adler-Bobenko-Suris and then present some extensions.
2010/12/03
13:30-14:30 Room #370 (Graduate School of Math. Sci. Bldg.)
Nalini Joshi (University of Sydney)
Geometric asymptotics of the first Painleve equation (ENGLISH)
Nalini Joshi (University of Sydney)
Geometric asymptotics of the first Painleve equation (ENGLISH)
[ Abstract ]
I will report on my recent collaboration with Hans Duistermaat on the geometry of the space of initial values of the first Painleve equation, which was first constructed by Okamoto. We show that highly accurate information about solutions can be found by utilizing the regularized and compactified space of initial values in Boutroux's coordinates. I will also describe numerical explorations based on this work obtained in collaboration with Holger Dullin.
I will report on my recent collaboration with Hans Duistermaat on the geometry of the space of initial values of the first Painleve equation, which was first constructed by Okamoto. We show that highly accurate information about solutions can be found by utilizing the regularized and compactified space of initial values in Boutroux's coordinates. I will also describe numerical explorations based on this work obtained in collaboration with Holger Dullin.
2010/08/06
15:00-16:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Matthieu Alfaro (University Montpellier 2)
Motion by mean curvature and Allen-Cahn equations (ENGLISH)
Matthieu Alfaro (University Montpellier 2)
Motion by mean curvature and Allen-Cahn equations (ENGLISH)
[ Abstract ]
After introducing the classical and the generalized motion by mean curvature, we give some connections with the singular limit of Allen-Cahn equations in both framework. New results and estimates shall be provided.
After introducing the classical and the generalized motion by mean curvature, we give some connections with the singular limit of Allen-Cahn equations in both framework. New results and estimates shall be provided.
2010/07/30
16:30-17:30 Room #370 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State University)
Global uniqueness in determining a coefficient by boundary data on small subboundaries (ENGLISH)
Oleg Emanouilov (Colorado State University)
Global uniqueness in determining a coefficient by boundary data on small subboundaries (ENGLISH)
[ Abstract ]
We consider the Dirichlet problem for the stationary two-dimensional Schroedinger equation. We discuss an inverse boundary value problem of determining the potential from a pair of all Dirichlet data supported in a subboundary S+ and all the corresponding Neumann data taken only on a subboundary S-. In the case where S+ = S- are the whole boundary, the data are the classical Dirichlet to Neumann map and there are many uniqueness results, while in the case where S+=S- is an arbitrary subboundary, Imanuvilov-Uhlmann-Yamamoto (2010) proves the uniqueness. In this talk, for the case where S+ and S- are not same, we prove the global uniqueness for this inverse problem under a condition only on the locations of S+, S-. We note that within the condition, S+ and S- can be arbitrarily small. The key of the proof is the construction of suitable complex geometrical optics solutions by a Carleman estimate with singular weight function.
We consider the Dirichlet problem for the stationary two-dimensional Schroedinger equation. We discuss an inverse boundary value problem of determining the potential from a pair of all Dirichlet data supported in a subboundary S+ and all the corresponding Neumann data taken only on a subboundary S-. In the case where S+ = S- are the whole boundary, the data are the classical Dirichlet to Neumann map and there are many uniqueness results, while in the case where S+=S- is an arbitrary subboundary, Imanuvilov-Uhlmann-Yamamoto (2010) proves the uniqueness. In this talk, for the case where S+ and S- are not same, we prove the global uniqueness for this inverse problem under a condition only on the locations of S+, S-. We note that within the condition, S+ and S- can be arbitrarily small. The key of the proof is the construction of suitable complex geometrical optics solutions by a Carleman estimate with singular weight function.
2010/07/28
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
及川 一誠 (東京大学大学院数理科学研究科)
定常移流拡散方程式に対するハイブリッド型不連続Galerkin法 (JAPANESE)
http://www.infsup.jp/utnas/
及川 一誠 (東京大学大学院数理科学研究科)
定常移流拡散方程式に対するハイブリッド型不連続Galerkin法 (JAPANESE)
[ Abstract ]
本講演では,ハイブリッド型不連続Galerkin(HDG)法による,定常移流拡散方程式の新しい数値計算スキームを紹介し,定式化や誤差評価,安定性等について述べる.新スキームの有効性を確認するために,数値計算例もいくつか示す.なお,講演前半は準備として,Poisson方程式に対するHDG法について解説する.
[ Reference URL ]本講演では,ハイブリッド型不連続Galerkin(HDG)法による,定常移流拡散方程式の新しい数値計算スキームを紹介し,定式化や誤差評価,安定性等について述べる.新スキームの有効性を確認するために,数値計算例もいくつか示す.なお,講演前半は準備として,Poisson方程式に対するHDG法について解説する.
http://www.infsup.jp/utnas/
2010/07/07
17:00-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
天野 要 (愛媛大学大学院理工学研究科)
代用電荷法による多重連結領域の数値等角写像 (JAPANESE)
http://www.infsup.jp/utnas/
天野 要 (愛媛大学大学院理工学研究科)
代用電荷法による多重連結領域の数値等角写像 (JAPANESE)
[ Abstract ]
多重連結領域の等角写像では,平行スリット領域,円弧スリット領域,放射スリット領域,円弧スリット円板領域,円弧スリット円環領域という5種の正準スリット領域が広く知られている(Nehari, 1952).遡って,Koebe(1916)はこれらを含む39種の正準スリット領域を挙げている.近年,このような多重連結領域の問題が新たに注目されている.代用電荷法を適用して,このような様々な等角写像の表現が簡潔で精度の高い近似写像関数を簡単に構成することができる.ここでは,非有界な多重連結領域から(実軸となす角を任意に指定した一般的な)直線スリット領域と,円弧放射スリット(混在)領域への場合中心に,代用電荷法による多重連結領域の数値等角写像の方法を紹介する.
[ Reference URL ]多重連結領域の等角写像では,平行スリット領域,円弧スリット領域,放射スリット領域,円弧スリット円板領域,円弧スリット円環領域という5種の正準スリット領域が広く知られている(Nehari, 1952).遡って,Koebe(1916)はこれらを含む39種の正準スリット領域を挙げている.近年,このような多重連結領域の問題が新たに注目されている.代用電荷法を適用して,このような様々な等角写像の表現が簡潔で精度の高い近似写像関数を簡単に構成することができる.ここでは,非有界な多重連結領域から(実軸となす角を任意に指定した一般的な)直線スリット領域と,円弧放射スリット(混在)領域への場合中心に,代用電荷法による多重連結領域の数値等角写像の方法を紹介する.
http://www.infsup.jp/utnas/
2010/06/24
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
村川 秀樹 (富山大学大学院理工学研究部)
非線形拡散問題の反応拡散系近似 (JAPANESE)
村川 秀樹 (富山大学大学院理工学研究部)
非線形拡散問題の反応拡散系近似 (JAPANESE)
[ Abstract ]
氷の融解・水の凝固の過程を記述するステファン問題、地下水の流れを表す多孔質媒体流方程式、2種生物種の競合問題における互いの動的な干渉作用を記述する重定-川崎-寺本交差拡散系など、様々な問題を含む非線形拡散問題を取り扱う。本講演では、非線形拡散問題の解が、拡散が線形である半線形反応拡散系の解により近似されることを示す。この結果は、非線形拡散問題の解構造が、ある種の半線形反応拡散系の中に再現されることを示唆するものである。一般に、非線形問題を扱うよりも半線形問題を取り扱う方が容易であるため、本研究は非線形問題の解析や数値解析に応用できることが期待される。
氷の融解・水の凝固の過程を記述するステファン問題、地下水の流れを表す多孔質媒体流方程式、2種生物種の競合問題における互いの動的な干渉作用を記述する重定-川崎-寺本交差拡散系など、様々な問題を含む非線形拡散問題を取り扱う。本講演では、非線形拡散問題の解が、拡散が線形である半線形反応拡散系の解により近似されることを示す。この結果は、非線形拡散問題の解構造が、ある種の半線形反応拡散系の中に再現されることを示唆するものである。一般に、非線形問題を扱うよりも半線形問題を取り扱う方が容易であるため、本研究は非線形問題の解析や数値解析に応用できることが期待される。
2010/06/23
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
村川 秀樹 (富山大学大学院理工学研究部(理学))
非線形交差拡散系の数値解法―反応拡散系近似理論の応用― (JAPANESE)
http://www.infsup.jp/utnas/
村川 秀樹 (富山大学大学院理工学研究部(理学))
非線形交差拡散系の数値解法―反応拡散系近似理論の応用― (JAPANESE)
[ Abstract ]
多成分反応拡散系において、他の成分同士、拡散が相互に依存しあっているときに、拡散が交差していると言い、そのような系は交差拡散系と呼ばれる。2種生物種の競合問題におけるお互いの動的な干渉作用を記述する重定-川崎-寺本モデルは非線形交差拡散を含む問題の代表例である。非線形交差拡散系に対する効果的な数値解法は個別の問題に対して構成され、解析されるのが現状である。現象のモデリングを行う場合など、パラメータの変更のみでなく、非線形項そのものを変えて多くの数値実験を行いたい場合がある。この様な状況に対応するために、汎用的で簡便な数値解法が望まれる。講演では、非線形交差拡散系を近似するある半線形反応拡散系を媒介することにより、そのような数値解法を導出、解析し、数値計算を通してその有用性を示す。時間が許せば、半線形反応拡散系を用いた退化放物型方程式の数値解法についても触れたい。
[ Reference URL ]多成分反応拡散系において、他の成分同士、拡散が相互に依存しあっているときに、拡散が交差していると言い、そのような系は交差拡散系と呼ばれる。2種生物種の競合問題におけるお互いの動的な干渉作用を記述する重定-川崎-寺本モデルは非線形交差拡散を含む問題の代表例である。非線形交差拡散系に対する効果的な数値解法は個別の問題に対して構成され、解析されるのが現状である。現象のモデリングを行う場合など、パラメータの変更のみでなく、非線形項そのものを変えて多くの数値実験を行いたい場合がある。この様な状況に対応するために、汎用的で簡便な数値解法が望まれる。講演では、非線形交差拡散系を近似するある半線形反応拡散系を媒介することにより、そのような数値解法を導出、解析し、数値計算を通してその有用性を示す。時間が許せば、半線形反応拡散系を用いた退化放物型方程式の数値解法についても触れたい。
http://www.infsup.jp/utnas/
2010/06/09
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
松本 純一 (産業技術総合研究所)
直交基底気泡関数有限要素法による流体解析と応用計算 (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
松本 純一 (産業技術総合研究所)
直交基底気泡関数有限要素法による流体解析と応用計算 (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2010/05/26
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
松家 敬介 (東京大学大学院数理科学研究科)
Existence and non-existence of global solutions for a discrete semilinear heat equation (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
松家 敬介 (東京大学大学院数理科学研究科)
Existence and non-existence of global solutions for a discrete semilinear heat equation (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2010/05/12
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
荻田 武史 (東京女子大学現代教養学部)
悪条件行列の高精度な分解法とその応用 (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
荻田 武史 (東京女子大学現代教養学部)
悪条件行列の高精度な分解法とその応用 (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2010/03/30
10:00-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Masahiro Yamamoto (University of Tokyo) 10:00-10:50
産学連携による新たな数学の課題:非整数階拡散方程式への誘い (JAPANESE)
Shu Nakamura (University of Tokyo) 11:00-11:50
量子力学のスペクトル・散乱理論における数学的手法 (JAPANESE)
Kazufumi Ito (University of Tokyo, North Carolina State University) 13:20-14:10
Semismooth Newton法の理論、及び応用 (JAPANESE)
Georg Weiss (University of Tokyo) 14:10-15:00
TBA (JAPANESE)
Masahiro Yamamoto (University of Tokyo) 10:00-10:50
産学連携による新たな数学の課題:非整数階拡散方程式への誘い (JAPANESE)
Shu Nakamura (University of Tokyo) 11:00-11:50
量子力学のスペクトル・散乱理論における数学的手法 (JAPANESE)
Kazufumi Ito (University of Tokyo, North Carolina State University) 13:20-14:10
Semismooth Newton法の理論、及び応用 (JAPANESE)
Georg Weiss (University of Tokyo) 14:10-15:00
TBA (JAPANESE)
2010/03/23
15:00-17:15 Room #370 (Graduate School of Math. Sci. Bldg.)
Mourad Bellassoued (Univ. of Bizerte) 15:00-16:00
Stability estimates for the anisotropic wave and Schrodinger equations from
the Dirichlet to Neumann map
On uniqueness in inverse elastic obstacle scattering
Mourad Bellassoued (Univ. of Bizerte) 15:00-16:00
Stability estimates for the anisotropic wave and Schrodinger equations from
the Dirichlet to Neumann map
[ Abstract ]
In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in a wave or Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the wave equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1.
Johannes Elschner (Weierstrass Institute Berlin, Germany) 16:15-17:15In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in a wave or Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the wave equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1.
On uniqueness in inverse elastic obstacle scattering
[ Abstract ]
The talk is on joint work with M. Yamamoto on the third and fourth exterior boundary value problems of linear isotropic elasticity. We present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves.
Our approach is essentially based on a reflection principle for the Navier equation.
The talk is on joint work with M. Yamamoto on the third and fourth exterior boundary value problems of linear isotropic elasticity. We present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves.
Our approach is essentially based on a reflection principle for the Navier equation.
2010/02/18
10:10-11:00 Room #122 (Graduate School of Math. Sci. Bldg.)
俣野 博 (数理科学)
空間的に非一様な場における進行波
俣野 博 (数理科学)
空間的に非一様な場における進行波
2010/02/18
11:00-11:50 Room #122 (Graduate School of Math. Sci. Bldg.)
野口 潤次郎 (数理科学)
岡の連接定理から一致の定理(点分布から分かるもの)まで
野口 潤次郎 (数理科学)
岡の連接定理から一致の定理(点分布から分かるもの)まで
2010/02/18
13:20-14:10 Room #122 (Graduate School of Math. Sci. Bldg.)
儀我 美一、大塚 岳 (数理科学、明治大学先端数理科学インスティチュート)
結晶界面の成長と偏微分方程式
儀我 美一、大塚 岳 (数理科学、明治大学先端数理科学インスティチュート)
結晶界面の成長と偏微分方程式
2010/02/18
14:10-14:40 Room #122 (Graduate School of Math. Sci. Bldg.)
古場 一 (数理科学)
成層の影響を考えたエクマン層の安定性について
古場 一 (数理科学)
成層の影響を考えたエクマン層の安定性について
2010/02/18
14:50-15:40 Room #122 (Graduate School of Math. Sci. Bldg.)
O. Iliev (フラウンホーファー産業数学研究所、ドイツ)
Flow and material simulation for industrial purposes
O. Iliev (フラウンホーファー産業数学研究所、ドイツ)
Flow and material simulation for industrial purposes
2010/01/07
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
LucRey-Bellet (Univ. Massachusetts)
Large deviations, Billiards, and Non-equilibrium Statistical Mechanics
LucRey-Bellet (Univ. Massachusetts)
Large deviations, Billiards, and Non-equilibrium Statistical Mechanics
[ Abstract ]
Large deviations have applications in many aspects of statistical mechanics. New applications for the steady states of non-equilibrium statistical mechanics have emerged during the past ten years and these applications deal with the fluctuations of the entropy production. After discussing some general aspects of entropy production we turn to concrete examples, in particular billiards with and without external forces and discuss large deviations theorems for such systems.
Large deviations have applications in many aspects of statistical mechanics. New applications for the steady states of non-equilibrium statistical mechanics have emerged during the past ten years and these applications deal with the fluctuations of the entropy production. After discussing some general aspects of entropy production we turn to concrete examples, in particular billiards with and without external forces and discuss large deviations theorems for such systems.
2009/12/08
17:30-19:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Giovanni Felder (ETH Zurich)
Gaudin subalgebras and stable rational curves. (ENGLISH)
Giovanni Felder (ETH Zurich)
Gaudin subalgebras and stable rational curves. (ENGLISH)
[ Abstract ]
We show that Abelian subalgebras of maximal dimensions spanned by generators of the n-th Kohno-Drinfeld Lie algebra are classified by the Grothendieck-Knudsen moduli space of stable rational curves with n+1 marked points. I will explain the relation with Gaudin integrable systems of statistical mechanics and the representation theory of the symmetric group in the formulation of Vershik and Okounkov. The talk is based on joint work with Leonardo Aguirre and Alexander Veselov.
We show that Abelian subalgebras of maximal dimensions spanned by generators of the n-th Kohno-Drinfeld Lie algebra are classified by the Grothendieck-Knudsen moduli space of stable rational curves with n+1 marked points. I will explain the relation with Gaudin integrable systems of statistical mechanics and the representation theory of the symmetric group in the formulation of Vershik and Okounkov. The talk is based on joint work with Leonardo Aguirre and Alexander Veselov.
2009/10/30
15:00-16:00 Room #370 (Graduate School of Math. Sci. Bldg.)
Shuai Lu (Johann Radon Institute)
Regularized total least squares: computational aspects and error bounds
Shuai Lu (Johann Radon Institute)
Regularized total least squares: computational aspects and error bounds
[ Abstract ]
For solving linear ill-posed problems, regularization methods are required when the right hand side and/or the operator are corrupted by some noise. In the present talk, regularized solutions are constructed using regularized total least squares and dual regularized total least squares. We discuss computational aspects and provide order optimal error bounds that characterize the accuracy of the regularized solutions. The results extend earlier results where the operator is exactly given. We also present some numerical experiments, which shed light on the relationship between RTLS, dual RTLS and the standard Tikhonov regularization.
For solving linear ill-posed problems, regularization methods are required when the right hand side and/or the operator are corrupted by some noise. In the present talk, regularized solutions are constructed using regularized total least squares and dual regularized total least squares. We discuss computational aspects and provide order optimal error bounds that characterize the accuracy of the regularized solutions. The results extend earlier results where the operator is exactly given. We also present some numerical experiments, which shed light on the relationship between RTLS, dual RTLS and the standard Tikhonov regularization.
2009/10/14
16:30-17:30 Room #370 (Graduate School of Math. Sci. Bldg.)
O. Emanouilov (Colorado State University)
Partial Cauchy data for general second order elliptic operators in two dimensions
O. Emanouilov (Colorado State University)
Partial Cauchy data for general second order elliptic operators in two dimensions
[ Abstract ]
We consider the problem of determining the coefficients of a first-order perturbation of the Laplacian in two dimensions by measuring the corresponding Cauchy data on an arbitrary open subset of the boundary. From this information we obtained a coupled PDE system of first order which the coefficients satisfy. As a corollary we show for the magnetic Schr"odinger equation that the magnetic field and the electric potential are uniquely determined by measuring the partial Cauchy data on an arbitrary part of the boundary. We also show that the coefficients of any real vector field perturbation of the Laplacian, the convection terms, are uniquely determined by their partial Cauchy data.
We consider the problem of determining the coefficients of a first-order perturbation of the Laplacian in two dimensions by measuring the corresponding Cauchy data on an arbitrary open subset of the boundary. From this information we obtained a coupled PDE system of first order which the coefficients satisfy. As a corollary we show for the magnetic Schr"odinger equation that the magnetic field and the electric potential are uniquely determined by measuring the partial Cauchy data on an arbitrary part of the boundary. We also show that the coefficients of any real vector field perturbation of the Laplacian, the convection terms, are uniquely determined by their partial Cauchy data.
2009/09/08
15:00-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
H.R.Thieme (Arizona State University)
Global compact attractors and their tripartition under persistence (ENGLISH)
H.R.Thieme (Arizona State University)
Global compact attractors and their tripartition under persistence (ENGLISH)
[ Abstract ]
The study of the dynamics of a semiflow (inertial manifolds, persistence) is largely facilitated if there is a global compact attractor, i.e. a compact invariant subset which attracts a sufficiently broad class of subsets of the state space.
Unfortunately, there in no uniform use of the concept of a global compact attractor in the literature: it has been used for a compact attractor of points, compact attractor of neighborhoods of compact sets, and compact attractor of bounded sets.
Persistence theory allows to discuss the long-term survival of populations in a dynamical systems framework. There is a two-way interaction between persistence and global compact attractors. On the one hand, the existence of a compact attractor of points helps to establish the persistence of the semiflow. On the other hand, the global attractor of a uniformly persistent semiflow divides into three invariant parts: an extinction attractor, a persistence attractor, and a set of orbits that connect the extinction to the persistence attractor. The persistence attractor has further interesting properties like local stability and connectedness. Examples are presented where the persistence attractor can be used to prove the global stability of the persistence equilibrium. (joint work with Hal L. Smith)
The study of the dynamics of a semiflow (inertial manifolds, persistence) is largely facilitated if there is a global compact attractor, i.e. a compact invariant subset which attracts a sufficiently broad class of subsets of the state space.
Unfortunately, there in no uniform use of the concept of a global compact attractor in the literature: it has been used for a compact attractor of points, compact attractor of neighborhoods of compact sets, and compact attractor of bounded sets.
Persistence theory allows to discuss the long-term survival of populations in a dynamical systems framework. There is a two-way interaction between persistence and global compact attractors. On the one hand, the existence of a compact attractor of points helps to establish the persistence of the semiflow. On the other hand, the global attractor of a uniformly persistent semiflow divides into three invariant parts: an extinction attractor, a persistence attractor, and a set of orbits that connect the extinction to the persistence attractor. The persistence attractor has further interesting properties like local stability and connectedness. Examples are presented where the persistence attractor can be used to prove the global stability of the persistence equilibrium. (joint work with Hal L. Smith)
2009/09/08
16:15-17:15 Room #123 (Graduate School of Math. Sci. Bldg.)
Glenn Webb (Vanderbilt University)
Analysis of a Model for Transfer Phenomena in Biological Populations (ENGLISH)
Glenn Webb (Vanderbilt University)
Analysis of a Model for Transfer Phenomena in Biological Populations (ENGLISH)
[ Abstract ]
We study the problem of transfer in a population structured by a continuum variable corresponding to the quantity being transferred. The transfer of the quantity occurs between individuals according to specified rules. The model is of Boltzmann type with kernel corresponding to the transfer process. We prove that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. We generalize the model by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that transfer is sufficiently small. We discuss an application of our model to cancer cell populations, in which individual cells exchange the surface protein P-glycoprotein, an important factor in acquired multidrug resistance against cancer chemotherapy.
We study the problem of transfer in a population structured by a continuum variable corresponding to the quantity being transferred. The transfer of the quantity occurs between individuals according to specified rules. The model is of Boltzmann type with kernel corresponding to the transfer process. We prove that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. We generalize the model by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that transfer is sufficiently small. We discuss an application of our model to cancer cell populations, in which individual cells exchange the surface protein P-glycoprotein, an important factor in acquired multidrug resistance against cancer chemotherapy.
2009/03/05
10:15-11:15 Room #270 (Graduate School of Math. Sci. Bldg.)
V. Isakov (Wichita State Univ.)
Carleman type estimates with two large parameters and applications to elasticity theory woth residual stress
V. Isakov (Wichita State Univ.)
Carleman type estimates with two large parameters and applications to elasticity theory woth residual stress
[ Abstract ]
We give Carleman estimates with two large parameters for general second order partial differential operators with real-valued coefficients.
We outline proofs based on differential quadratic forms and Fourier analysis. As an application, we give Carleman estimates for (anisotropic)elasticity system with residual stress and discuss applications to control theory and inverse problems.
We give Carleman estimates with two large parameters for general second order partial differential operators with real-valued coefficients.
We outline proofs based on differential quadratic forms and Fourier analysis. As an application, we give Carleman estimates for (anisotropic)elasticity system with residual stress and discuss applications to control theory and inverse problems.
