## GCOEセミナー

過去の記録 ～03/27｜次回の予定｜今後の予定 03/28～

**過去の記録**

### 2014年03月14日(金)

16:00-16:50 数理科学研究科棟(駒場) 118号室

A new finite difference scheme based on staggered grids for Navier Stokes equations (ENGLISH)

**Kazufumi Ito 氏**(North Carolina State Univ.)A new finite difference scheme based on staggered grids for Navier Stokes equations (ENGLISH)

[ 講演概要 ]

We develop a new method that uses the staggered grid only for the pressure node, i.e., the pressure gird is the center of the square cell and the velocities are at the node. The advantage of the proposed method compared to the standard staggered grid methods is that it is very straight forward to treat the boundary conditions for the velocity field, the fluid structure interaction, and to deal with the multiphase flow using the immersed interface methods. We present our analysis and numerical tests.

We develop a new method that uses the staggered grid only for the pressure node, i.e., the pressure gird is the center of the square cell and the velocities are at the node. The advantage of the proposed method compared to the standard staggered grid methods is that it is very straight forward to treat the boundary conditions for the velocity field, the fluid structure interaction, and to deal with the multiphase flow using the immersed interface methods. We present our analysis and numerical tests.

### 2014年03月14日(金)

17:00-17:50 数理科学研究科棟(駒場) 118号室

Efficient Domain Decomposition Methods for a Class of Linear and Nonlinear Inverse Problems (ENGLISH)

**Jun Zou 氏**(The Chinese University of Hong Kong)Efficient Domain Decomposition Methods for a Class of Linear and Nonlinear Inverse Problems (ENGLISH)

[ 講演概要 ]

In this talk we shall present several new domain decomposition methods for solving some linear and nonlinear inverse problems. The motivations and derivations of the methods will be discussed, and numerical experiments will be demonstrated.

In this talk we shall present several new domain decomposition methods for solving some linear and nonlinear inverse problems. The motivations and derivations of the methods will be discussed, and numerical experiments will be demonstrated.

### 2014年03月13日(木)

17:00-18:00 数理科学研究科棟(駒場) 122号室

STABILITY IN THE OBSTACLE PROBLEM FOR A SHALLOW SHELL (ENGLISH)

[ 参考URL ]

http://fmsp.ms.u-tokyo.ac.jp/bm02.pdf

**Bernadette Miara 氏**(Univ. Paris-Est)STABILITY IN THE OBSTACLE PROBLEM FOR A SHALLOW SHELL (ENGLISH)

[ 参考URL ]

http://fmsp.ms.u-tokyo.ac.jp/bm02.pdf

### 2014年03月12日(水)

15:00-17:00 数理科学研究科棟(駒場) 126号室

When size does matter: Ontogenetic symmetry and asymmetry in energetics (ENGLISH)

http://staff.science.uva.nl/~aroos/

**Andre M. de Roos 氏**(University of Amsterdam)When size does matter: Ontogenetic symmetry and asymmetry in energetics (ENGLISH)

[ 講演概要 ]

Body size (≡ biomass) is the dominant determinant of population dynamical processes such as giving birth or dying in almost all species, with often drastically different behaviour occurring in different parts of the growth trajectory, while the latter is largely determined by food availability at the different life stages. This leads to the question under what conditions unstructured population models, formulated in terms of total population biomass, still do a fair job. To contribute to answering this question we first analyze the conditions under which a size-structured model collapses to a dynamically equivalent unstructured one in terms of total biomass. The only biologically meaningful case where this occurs is when body size does not affect any of the population dynamic processes, this is the case if and only if the mass-specific ingestion rate, the mass-specific biomass production and the mortality rate of the individuals are independent of size, a condition to which we refer as “ontogenetic symmetry”. Intriguingly, under ontogenetic symmetry the equilibrium biomass-body size spectrum is proportional to 1/size, a form that has been conjectured for marine size spectra and subsequently has been used as prior assumption in theoretical papers dealing with the latter. As a next step we consider an archetypical class of models in which reproduction takes over from growth upon reaching an adult body size, in order to determine how quickly discrepancies from ontogenetic symmetry lead to relevant novel population dynamical phenomena. The phenomena considered are biomass overcompensation, when additional imposed mortality leads, rather unexpectedly, to an increase in the equilibrium biomass of either the juveniles or the adults (a phenomenon with potentially big consequences for predators of the species), and the occurrence of two types of size-structure driven oscillations, juvenile-driven cycles with separated extended cohorts, and adult-driven cycles in which periodically a front of relatively steeply decreasing frequencies moves up the size distribution. A small discrepancy from symmetry can already lead to biomass overcompensation; size-structure driven cycles only occur for somewhat larger discrepancies.

[ 参考URL ]Body size (≡ biomass) is the dominant determinant of population dynamical processes such as giving birth or dying in almost all species, with often drastically different behaviour occurring in different parts of the growth trajectory, while the latter is largely determined by food availability at the different life stages. This leads to the question under what conditions unstructured population models, formulated in terms of total population biomass, still do a fair job. To contribute to answering this question we first analyze the conditions under which a size-structured model collapses to a dynamically equivalent unstructured one in terms of total biomass. The only biologically meaningful case where this occurs is when body size does not affect any of the population dynamic processes, this is the case if and only if the mass-specific ingestion rate, the mass-specific biomass production and the mortality rate of the individuals are independent of size, a condition to which we refer as “ontogenetic symmetry”. Intriguingly, under ontogenetic symmetry the equilibrium biomass-body size spectrum is proportional to 1/size, a form that has been conjectured for marine size spectra and subsequently has been used as prior assumption in theoretical papers dealing with the latter. As a next step we consider an archetypical class of models in which reproduction takes over from growth upon reaching an adult body size, in order to determine how quickly discrepancies from ontogenetic symmetry lead to relevant novel population dynamical phenomena. The phenomena considered are biomass overcompensation, when additional imposed mortality leads, rather unexpectedly, to an increase in the equilibrium biomass of either the juveniles or the adults (a phenomenon with potentially big consequences for predators of the species), and the occurrence of two types of size-structure driven oscillations, juvenile-driven cycles with separated extended cohorts, and adult-driven cycles in which periodically a front of relatively steeply decreasing frequencies moves up the size distribution. A small discrepancy from symmetry can already lead to biomass overcompensation; size-structure driven cycles only occur for somewhat larger discrepancies.

http://staff.science.uva.nl/~aroos/

### 2014年03月11日(火)

17:00-18:00 数理科学研究科棟(駒場) 118号室

Inverse problem for the waves : stability and convergence matters (ENGLISH)

**Lucie Baudouin 氏**(LAAS-CNRS, equipe MAC)Inverse problem for the waves : stability and convergence matters (ENGLISH)

[ 講演概要 ]

This talk aims to present some recent works in collaboration with Maya de Buhan, Sylvain Ervedoza and Axel Osses regarding an inverse problem for the wave equation. More specifically, we study the determination of the potential in a wave equation with given Dirichlet boundary data from a measurement of the flux of the solution on a part of the boundary. On the one hand, we will focus on the question of convergence of the space semi-discrete inverse problems toward their continuous counterpart. Several uniqueness and stability results are available in the literature about the continuous setting of the inverse problem of determination of a potential in the wave equation. In particular, we can mention a Lipschitz stability result under a classical geometric condition obtained by Imanuvilov and Yamamoto, and a logarithmic stability result obtained by Bellassoued when the observation measurement is made on an arbitrary part of the boundary. In both situations, we can design a numerical process for which convergence results are proved. The analysis we conduct is based on discrete Carleman estimates, either for the hyperbolic or for the elliptic operator, in which case we shall use a result of Boyer, Hubert and Le Rousseau. On the other hand, still considering the same inverse problem, we will present a new reconstruction algorithm of the potential. The design and convergence of the algorithm are based on the Carleman estimates for the waves previously used to prove the Lipschitz stability. We will finally give some simple illustrative numerical simulations for 1-d problems.

This talk aims to present some recent works in collaboration with Maya de Buhan, Sylvain Ervedoza and Axel Osses regarding an inverse problem for the wave equation. More specifically, we study the determination of the potential in a wave equation with given Dirichlet boundary data from a measurement of the flux of the solution on a part of the boundary. On the one hand, we will focus on the question of convergence of the space semi-discrete inverse problems toward their continuous counterpart. Several uniqueness and stability results are available in the literature about the continuous setting of the inverse problem of determination of a potential in the wave equation. In particular, we can mention a Lipschitz stability result under a classical geometric condition obtained by Imanuvilov and Yamamoto, and a logarithmic stability result obtained by Bellassoued when the observation measurement is made on an arbitrary part of the boundary. In both situations, we can design a numerical process for which convergence results are proved. The analysis we conduct is based on discrete Carleman estimates, either for the hyperbolic or for the elliptic operator, in which case we shall use a result of Boyer, Hubert and Le Rousseau. On the other hand, still considering the same inverse problem, we will present a new reconstruction algorithm of the potential. The design and convergence of the algorithm are based on the Carleman estimates for the waves previously used to prove the Lipschitz stability. We will finally give some simple illustrative numerical simulations for 1-d problems.

### 2014年03月10日(月)

13:30-15:00 数理科学研究科棟(駒場) 123号室

The two-dimensional random walk in an isotropic random environment (ENGLISH)

**Erwin Bolthausen 氏**(University of Zurich)The two-dimensional random walk in an isotropic random environment (ENGLISH)

### 2014年03月10日(月)

17:00-18:00 数理科学研究科棟(駒場) 118号室

ELASTIC WAVES IN STRONGLY HETEROGENEOUS PLATES (ENGLISH)

[ 参考URL ]

http://fmsp.ms.u-tokyo.ac.jp/bm01.pdf

**Bernadette Miara 氏**(Univ. Paris-Est)ELASTIC WAVES IN STRONGLY HETEROGENEOUS PLATES (ENGLISH)

[ 参考URL ]

http://fmsp.ms.u-tokyo.ac.jp/bm01.pdf

### 2014年03月06日(木)

10:10-11:00 数理科学研究科棟(駒場) 002号室

このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補

The Mathematical Model for the Contamination Problems and Related Inverse Problems (ENGLISH)

このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補

**J. Cheng 氏**(Fudan Univ.)The Mathematical Model for the Contamination Problems and Related Inverse Problems (ENGLISH)

[ 講演概要 ]

In this talk, we discuss the motivation for the study of the abnormal diffusion models for the contamination problems. From the practical point of view, several inverse problems proposed and studied Theoretic results, for example, the uniqueness and stability are shown. The possibility of the application of these studies is mentioned.

In this talk, we discuss the motivation for the study of the abnormal diffusion models for the contamination problems. From the practical point of view, several inverse problems proposed and studied Theoretic results, for example, the uniqueness and stability are shown. The possibility of the application of these studies is mentioned.

### 2014年03月06日(木)

11:10-12:00 数理科学研究科棟(駒場) 002号室

このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補

Inverse problems with fractional derivatives in the space variable (ENGLISH)

このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補

**W. Rundell 氏**(Texas A&M Univ.)Inverse problems with fractional derivatives in the space variable (ENGLISH)

[ 講演概要 ]

This talk will look at some classical inverse problems where the highest order term in the spatial direction is replaced by a fractional derivative. There are again some surprising results over what is known in the usual case of integer order derivatives but also quite different from the case of fractional diffusion in the time variable. The talk will give some answers, but pose many more open problems.

This talk will look at some classical inverse problems where the highest order term in the spatial direction is replaced by a fractional derivative. There are again some surprising results over what is known in the usual case of integer order derivatives but also quite different from the case of fractional diffusion in the time variable. The talk will give some answers, but pose many more open problems.

### 2014年03月06日(木)

14:30-15:20 数理科学研究科棟(駒場) 002号室

このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補

Neutral-fractional diffusion-wave equation and some properties of its fundamental solution (ENGLISH)

このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補

**Y. Luchko 氏**(Beuth Technical University of Applied Sciences)Neutral-fractional diffusion-wave equation and some properties of its fundamental solution (ENGLISH)

[ 講演概要 ]

Recently, the so called neutral-fractional diffusion-wave equation was introduced and analysed in the case of one spatial variable. In contrast to the fractional diffusion of diffusion-wave equations, the neutral-fractional diffusion-wave equation contains fractional derivatives of the same order both in space and in time. The fundamental solution of the neutral-fractional diffusion-wave equation was shown to exhibit properties of both the solutions of the diffusion equation and those of the wave equation.

In the one-dimensional case, the fundamental solution of the neutral-fractional diffusion-wave equation can be interpreted as a spatial probability density function evolving in time. At the same time, it can be treated as a damped wave whose amplitude maximum and the gravity and mass centres propagate with the constant velocities that depend just on the equation order.

In this talk, the problems mentioned above are considered for the multi- dimensional neutral-fractional diffusion-wave equation. To illustrate analytical findings, some results of numerical calculations and plots are presented.

Recently, the so called neutral-fractional diffusion-wave equation was introduced and analysed in the case of one spatial variable. In contrast to the fractional diffusion of diffusion-wave equations, the neutral-fractional diffusion-wave equation contains fractional derivatives of the same order both in space and in time. The fundamental solution of the neutral-fractional diffusion-wave equation was shown to exhibit properties of both the solutions of the diffusion equation and those of the wave equation.

In the one-dimensional case, the fundamental solution of the neutral-fractional diffusion-wave equation can be interpreted as a spatial probability density function evolving in time. At the same time, it can be treated as a damped wave whose amplitude maximum and the gravity and mass centres propagate with the constant velocities that depend just on the equation order.

In this talk, the problems mentioned above are considered for the multi- dimensional neutral-fractional diffusion-wave equation. To illustrate analytical findings, some results of numerical calculations and plots are presented.

### 2014年03月06日(木)

16:20-17:10 数理科学研究科棟(駒場) 002号室

このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補

New kind of observations in an inverse parabolic problem (ENGLISH)

このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補

**M. Cristofol 氏**(Aix-Marseille Univ.)New kind of observations in an inverse parabolic problem (ENGLISH)

[ 講演概要 ]

In this talk, I analyze the inverse problem of determining the reaction term f(x,u) in reaction-diffusion equations of the form ¥partial_t u-D¥partial_{xx}u = f(x,u), where f is assumed to be periodic with respect to x in R. Starting from a family of exponentially decaying initial conditions u_{0,¥lambda}, I will show that the solutions u_¥lambda of this equation propagate with constant asymptotic spreading speeds w_¥lambda. The main result shows that the linearization of f around the steady state 0,¥partial_u f(x,0), is uniquely determined (up to a symmetry) among a subset of piecewise linear functions, by the observation of the asymptotic spreading speeds w_¥lambda.

In this talk, I analyze the inverse problem of determining the reaction term f(x,u) in reaction-diffusion equations of the form ¥partial_t u-D¥partial_{xx}u = f(x,u), where f is assumed to be periodic with respect to x in R. Starting from a family of exponentially decaying initial conditions u_{0,¥lambda}, I will show that the solutions u_¥lambda of this equation propagate with constant asymptotic spreading speeds w_¥lambda. The main result shows that the linearization of f around the steady state 0,¥partial_u f(x,0), is uniquely determined (up to a symmetry) among a subset of piecewise linear functions, by the observation of the asymptotic spreading speeds w_¥lambda.

### 2014年02月28日(金)

13:00-14:00 数理科学研究科棟(駒場) 002号室

Probing for inclusions for heat conductive bodies. Time independent and time dependent cases (ENGLISH)

**Patricia Gaitan 氏**(Aix-Marseille University)Probing for inclusions for heat conductive bodies. Time independent and time dependent cases (ENGLISH)

[ 講演概要 ]

This work deals with an inverse boundary value problem arising from the equation of heat conduction. Mathematical theory and algorithm is described in dimensions 1{3 for probing the discontinuous part of the conductivity from local temperature and heat ow measurements at the boundary. The ap- proach is based on the use of complex spherical waves, and no knowledge is needed about the initial temperature distribution. In dimension two we show how conformal transformations can be used for probing deeper than is pos- sible with discs. Results from numerical experiments in the one-dimensional case are reported, suggesting that the method is capable of recovering loca- tions of discontinuities approximately from noisy data.

For moving inclusions, we consider an inverse boundary value problem for the heat equation on the interval (0; 1), where the heat conductivity (t; x) is piecewise constant and the point of discontinuity depends on time : (t; x) = k2 (0 < x < s(t)), (t; x) = 1 (s(t) < x < 1). Firstly we show that k and s(t) on the time interval [0; T] are determined from the partial Dirichlet- to-Neumann map : u(t; 1) ! @xu(t; 1); 0 < t < T, u(t; x) being the solu- tion to the heat equation such that u(t; 0) = 0, independently of the initial data u(0; x). Secondly we show that the partial Dirichlet-to-Neumann map u(t; 0) ! @xu(t; 1); 0 < t < T, u(t; x) being the solution to the heat equation such that u(t; 1) = 0, determines at most two couples (k; s(t)) on the time interval [0; T], independently of the initial data u(0; x).

This work deals with an inverse boundary value problem arising from the equation of heat conduction. Mathematical theory and algorithm is described in dimensions 1{3 for probing the discontinuous part of the conductivity from local temperature and heat ow measurements at the boundary. The ap- proach is based on the use of complex spherical waves, and no knowledge is needed about the initial temperature distribution. In dimension two we show how conformal transformations can be used for probing deeper than is pos- sible with discs. Results from numerical experiments in the one-dimensional case are reported, suggesting that the method is capable of recovering loca- tions of discontinuities approximately from noisy data.

For moving inclusions, we consider an inverse boundary value problem for the heat equation on the interval (0; 1), where the heat conductivity (t; x) is piecewise constant and the point of discontinuity depends on time : (t; x) = k2 (0 < x < s(t)), (t; x) = 1 (s(t) < x < 1). Firstly we show that k and s(t) on the time interval [0; T] are determined from the partial Dirichlet- to-Neumann map : u(t; 1) ! @xu(t; 1); 0 < t < T, u(t; x) being the solu- tion to the heat equation such that u(t; 0) = 0, independently of the initial data u(0; x). Secondly we show that the partial Dirichlet-to-Neumann map u(t; 0) ! @xu(t; 1); 0 < t < T, u(t; x) being the solution to the heat equation such that u(t; 1) = 0, determines at most two couples (k; s(t)) on the time interval [0; T], independently of the initial data u(0; x).

### 2014年02月28日(金)

11:00-12:00 数理科学研究科棟(駒場) 002号室

Minimal time for the null controllability of parabolic systems: the effect of the index of condensation of complex sequences (ENGLISH)

**Assia Benabdallah 氏**(Aix-Marseille University)Minimal time for the null controllability of parabolic systems: the effect of the index of condensation of complex sequences (ENGLISH)

### 2014年02月27日(木)

17:00-18:00 数理科学研究科棟(駒場) 370号室

A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part II: for a an anisotropic elliptic operator. (ENGLISH)

**Yves Dermenjian 氏**(Univ. of Marseille)A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part II: for a an anisotropic elliptic operator. (ENGLISH)

### 2014年02月18日(火)

17:00-18:00 数理科学研究科棟(駒場) 370号室

A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part I: for a stratified parabolic operator. (ENGLISH)

**Yves Dermenjian 氏**(Univ. of Marseille)A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part I: for a stratified parabolic operator. (ENGLISH)

### 2014年02月03日(月)

16:00-17:00 数理科学研究科棟(駒場) 118号室

On the influence of the coupling on the dynamics of under-observed cascade systems of PDE’s (ENGLISH)

**Fatiha Alabau 氏**(University of Lorraine)On the influence of the coupling on the dynamics of under-observed cascade systems of PDE’s (ENGLISH)

[ 講演概要 ]

We consider observability of coupled dynamical systems of hyperbolic and parabolic type when the number of observations is strictly less that the number of unknowns. A main issue is to understand how the lack of observations of certain components is compensated by the coupling information. This talk will present a mathematical approach based on energy methods and some recent positive and negative results on these questions.

We consider observability of coupled dynamical systems of hyperbolic and parabolic type when the number of observations is strictly less that the number of unknowns. A main issue is to understand how the lack of observations of certain components is compensated by the coupling information. This talk will present a mathematical approach based on energy methods and some recent positive and negative results on these questions.

### 2014年02月03日(月)

17:00-18:00 数理科学研究科棟(駒場) 118号室

Compactness estimates for Hamilton-Jacobi equations (ENGLISH)

**Piermarco Cannarsa 氏**(University of Rome Tor Vergata)Compactness estimates for Hamilton-Jacobi equations (ENGLISH)

[ 講演概要 ]

For scalar conservations laws in one space dimension, P. Lax was the first to obtain compactness properties of the solution semigroup. Such properties were subsequently analyzed by several authors in quantitative terms using Kolmogorov's entropy. In this talk, we shall explain how to adapt such approach to the Hopf-Lax semigroup of solutions to first order Hamilton-Jacobi equations in arbitrary space dimension, and discuss related controllability issues.

For scalar conservations laws in one space dimension, P. Lax was the first to obtain compactness properties of the solution semigroup. Such properties were subsequently analyzed by several authors in quantitative terms using Kolmogorov's entropy. In this talk, we shall explain how to adapt such approach to the Hopf-Lax semigroup of solutions to first order Hamilton-Jacobi equations in arbitrary space dimension, and discuss related controllability issues.

### 2014年01月28日(火)

16:30-18:00 数理科学研究科棟(駒場) 128号室

Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)

http://agusta.ms.u-tokyo.ac.jp/analysis.html

**Arnaud Ducrot 氏**(University of Bordeaux)Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)

[ 講演概要 ]

In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.

[ 参考URL ]In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.

http://agusta.ms.u-tokyo.ac.jp/analysis.html

### 2014年01月20日(月)

16:00-17:00 数理科学研究科棟(駒場) 118号室

Increasing stability in the inverse problems for the Helmholtz type prposed equations (ENGLISH)

**Victor Isakov 氏**(The Wichita State University)Increasing stability in the inverse problems for the Helmholtz type prposed equations (ENGLISH)

[ 講演概要 ]

We report on new stability estimates for recovery of the near field from the prposed scattering amplitude prposed and for Schroedinger potential from the Dirichlet-to Neumann map. In these prposed esrtimates prposed unstable (logarithmic part) goes to zero as the wave number grows. Proofs prposed are using prposed new bounds for Hankel functions and complex and real geometrical optics prposed solutions.

We report on new stability estimates for recovery of the near field from the prposed scattering amplitude prposed and for Schroedinger potential from the Dirichlet-to Neumann map. In these prposed esrtimates prposed unstable (logarithmic part) goes to zero as the wave number grows. Proofs prposed are using prposed new bounds for Hankel functions and complex and real geometrical optics prposed solutions.

### 2014年01月15日(水)

16:00-17:00 数理科学研究科棟(駒場) 370号室

Increasing stability of the continuation for the Helmholtz type equations (ENGLISH)

**Victor Isakov 氏**(The Wichita State University)Increasing stability of the continuation for the Helmholtz type equations (ENGLISH)

[ 講演概要 ]

We derive conditional stability estimates for the Helmholtz type equations which are becoming of Lipschitz type for large frequencies/wave numbers. Proofs use splitting solutions into low and high frequencies parts where we use energy (in particular) Carleman estimates. We discuss numerical confirmation and open problems.

We derive conditional stability estimates for the Helmholtz type equations which are becoming of Lipschitz type for large frequencies/wave numbers. Proofs use splitting solutions into low and high frequencies parts where we use energy (in particular) Carleman estimates. We discuss numerical confirmation and open problems.

### 2014年01月15日(水)

17:00-18:00 数理科学研究科棟(駒場) 370号室

A numerical method for solving the inverse heat conduction problem without initial value (ENGLISH)

**Jin Cheng 氏**(Fudan University)A numerical method for solving the inverse heat conduction problem without initial value (ENGLISH)

[ 講演概要 ]

In this talk, we will present some results for the inverse heat conduction problem for the heat equation of determining a boundary value at in an unreachable part of the boundary. The main difficulty for this problem is that the initial value is unknown by the practical reason. A new method is prposed to solve this problem and the nuemrical tests show the effective of this method. Some theoretic analysis will be presented. This is a joint work with J Nakagawa, YB Wang, M Yamamoto.

In this talk, we will present some results for the inverse heat conduction problem for the heat equation of determining a boundary value at in an unreachable part of the boundary. The main difficulty for this problem is that the initial value is unknown by the practical reason. A new method is prposed to solve this problem and the nuemrical tests show the effective of this method. Some theoretic analysis will be presented. This is a joint work with J Nakagawa, YB Wang, M Yamamoto.

### 2014年01月14日(火)

15:00-16:00 数理科学研究科棟(駒場) 118号室

Calderon problem for Maxwell's equations in cylindrical domain (ENGLISH)

**Oleg Emanouilov 氏**(Colorado State University)Calderon problem for Maxwell's equations in cylindrical domain (ENGLISH)

[ 講演概要 ]

We prove some uniqueness results in determination of the conductivity, the permeability and the permittivity of Maxwell's equations from partial Dirichlet-to-Neumann map.

We prove some uniqueness results in determination of the conductivity, the permeability and the permittivity of Maxwell's equations from partial Dirichlet-to-Neumann map.

### 2013年12月25日(水)

16:00-17:00 数理科学研究科棟(駒場) 270号室

Nonsmooth Nonconvex Optimization Problems (ENGLISH)

**Kazufumi Ito 氏**(North Carolina State University)Nonsmooth Nonconvex Optimization Problems (ENGLISH)

[ 講演概要 ]

A general class of nonsmooth nonconvex optimization problems is discussed. A general existence theory of solutions, the Lagrange multiplier theory and sensitivity analysis of the optimal value function are developed. Concrete examples are presented to demonstrate the applicability of our approach.

A general class of nonsmooth nonconvex optimization problems is discussed. A general existence theory of solutions, the Lagrange multiplier theory and sensitivity analysis of the optimal value function are developed. Concrete examples are presented to demonstrate the applicability of our approach.

### 2013年12月20日(金)

15:00-16:00 数理科学研究科棟(駒場) 118号室

Determination of the magnetic field in an anisotropic Schrodinger equation (ENGLISH)

**Mourad Bellassoued 氏**(Bizerte University)Determination of the magnetic field in an anisotropic Schrodinger equation (ENGLISH)

[ 講演概要 ]

This talk is devoted to the study of the following inverse boundary value problem: given a Riemannian manifold with boundary, determine the magnetic potential in a dynamical Schroedinger equation in a magnetic field from the observations made at the boundary.

This talk is devoted to the study of the following inverse boundary value problem: given a Riemannian manifold with boundary, determine the magnetic potential in a dynamical Schroedinger equation in a magnetic field from the observations made at the boundary.

### 2013年11月28日(木)

17:00-18:00 数理科学研究科棟(駒場) 470号室

Inverse problem for the Maxwell equations (ENGLISH)

**Oleg Emanouilov 氏**(Colorado State Univ.)Inverse problem for the Maxwell equations (ENGLISH)

[ 講演概要 ]

We consider an analog of Caderon's problem for the system of Maxwell equations in a cylindrical domain.

Under some geometrical assumptions on domain we show that from the partial data one can recover the complete set of parameters.

We consider an analog of Caderon's problem for the system of Maxwell equations in a cylindrical domain.

Under some geometrical assumptions on domain we show that from the partial data one can recover the complete set of parameters.