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過去の記録 ～04/15｜次回の予定｜今後の予定 04/16～
過去の記録
2009年03月05日(木)
11:15-12:15 数理科学研究科棟(駒場) 270号室
J. Ralston 氏 (UCLA)
Determining moving boundaries from Cauchy data on remote surfaces
J. Ralston 氏 (UCLA)
Determining moving boundaries from Cauchy data on remote surfaces
[ 講演概要 ]
We consider wave equations in domains with time-dependent boundaries (moving obstacles) contained in a fixed cylinder for all time. We give sufficient conditions for the determination of the moving boundary from the Cauchy data on part of the boundary of the cylinder. We also study the related problem of reachability of the moving boundary by time-like curves from the boundary of the cylinder.
We consider wave equations in domains with time-dependent boundaries (moving obstacles) contained in a fixed cylinder for all time. We give sufficient conditions for the determination of the moving boundary from the Cauchy data on part of the boundary of the cylinder. We also study the related problem of reachability of the moving boundary by time-like curves from the boundary of the cylinder.
2009年03月04日(水)
15:00-16:00 数理科学研究科棟(駒場) 270号室
P. Gaitan (with H. Isozaki and O. Poisson) 氏 (Univ. Marseille)
Probing for inclusions for the heat equation with complex
spherical waves
P. Gaitan (with H. Isozaki and O. Poisson) 氏 (Univ. Marseille)
Probing for inclusions for the heat equation with complex
spherical waves
2009年03月04日(水)
16:15-17:15 数理科学研究科棟(駒場) 270号室
M. Cristofol 氏 (Univ. Marseille)
Coefficient reconstruction from partial measurements in a heterogeneous
equation of FKPP type
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/abstractTokyo.pdf
M. Cristofol 氏 (Univ. Marseille)
Coefficient reconstruction from partial measurements in a heterogeneous
equation of FKPP type
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/abstractTokyo.pdf
2009年03月03日(火)
16:15-17:15 数理科学研究科棟(駒場) 270号室
O. Poisson 氏 (Univ. Marseille)
Carleman estimates for the heat equation with discontinuous diffusion coefficients and applications
O. Poisson 氏 (Univ. Marseille)
Carleman estimates for the heat equation with discontinuous diffusion coefficients and applications
[ 講演概要 ]
We consider a heat equation in a bounded domain. We assume that the coefficient depends on the spatial variable and admits a discontinuity across an interface. We prove a Carleman estimate for the solution of the above heat equation without assumptions on signs of the jump of the coefficient.
We consider a heat equation in a bounded domain. We assume that the coefficient depends on the spatial variable and admits a discontinuity across an interface. We prove a Carleman estimate for the solution of the above heat equation without assumptions on signs of the jump of the coefficient.
2009年03月03日(火)
15:00-16:00 数理科学研究科棟(駒場) 270号室
Y. Dermenjian 氏 (Univ. Marseille)
Controllability of the heat equation in a stratified media : a consequence of its spectral structure.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/DermenjianTokyo2009.pdf
Y. Dermenjian 氏 (Univ. Marseille)
Controllability of the heat equation in a stratified media : a consequence of its spectral structure.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/DermenjianTokyo2009.pdf
2009年03月02日(月)
15:00-16:00 数理科学研究科棟(駒場) 270号室
Bernd Hofmann 氏 (Chemnitz University of Technology)
Convergence rates for nonlinear ill-posed problems based on variational inequalities expressing source conditions
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/hofmann.pdf
Bernd Hofmann 氏 (Chemnitz University of Technology)
Convergence rates for nonlinear ill-posed problems based on variational inequalities expressing source conditions
[ 講演概要 ]
Twenty years ago Engl, Kunisch and Neubauer presented the fundamentals of a systematic theory for convergence rates in Tikhonov regularization
[ 参考URL ]Twenty years ago Engl, Kunisch and Neubauer presented the fundamentals of a systematic theory for convergence rates in Tikhonov regularization
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/hofmann.pdf
2009年02月26日(木)
15:00-16:00 数理科学研究科棟(駒場) 470号室
時間が15:00～16:00に変わりましたのでご注意ください。
Jijun Liu 氏 (Southeast University, P.R.China)
Reconstruction of biological tissue conductivity by MREIT technique
時間が15:00～16:00に変わりましたのでご注意ください。
Jijun Liu 氏 (Southeast University, P.R.China)
Reconstruction of biological tissue conductivity by MREIT technique
[ 講演概要 ]
Magnetic resonance electrical impedance tomography (MREIT) is a new technique in medical imaging, which aims to provide electrical conductivity images of biological tissue. Compared with the traditional electrical impedance tomography (EIT)model, MREIT reconstructs the interior conductivity from the deduced magnetic field information inside the tissue. Since the late 1990s, MREIT imaging techniques have made significant progress experimentally and numerically. However, the theoretical analysis on the MREIT algorithms is still at the initial stage. In this talk, we will give a state of the art of the MREIT technique and to concern the convergence property as well as the numerical implementation of harmonic B_z algorithm and nonlinear integral equation algorithm. We present some late advances in the convergence issues of MREIT algorithm. Some open problems related to the noisy effects and the numerical implementations are also given.
Magnetic resonance electrical impedance tomography (MREIT) is a new technique in medical imaging, which aims to provide electrical conductivity images of biological tissue. Compared with the traditional electrical impedance tomography (EIT)model, MREIT reconstructs the interior conductivity from the deduced magnetic field information inside the tissue. Since the late 1990s, MREIT imaging techniques have made significant progress experimentally and numerically. However, the theoretical analysis on the MREIT algorithms is still at the initial stage. In this talk, we will give a state of the art of the MREIT technique and to concern the convergence property as well as the numerical implementation of harmonic B_z algorithm and nonlinear integral equation algorithm. We present some late advances in the convergence issues of MREIT algorithm. Some open problems related to the noisy effects and the numerical implementations are also given.
2009年02月13日(金)
14:00-14:45 数理科学研究科棟(駒場) 270号室
Johannes Elschner 氏 (Weierstrass Institute)
Direct and inverse problems in fluid-solid interaction
Johannes Elschner 氏 (Weierstrass Institute)
Direct and inverse problems in fluid-solid interaction
[ 講演概要 ]
We consider the interaction between an elastic body and a compressible inviscid fluid, which occupies the unbounded exterior domain. The direct problem is to determine the scattered pressure field in the fluid domain as well as the displacement field in the elastic body, while the inverse problem is to reconstruct the shape of the elastic body from the far field pattern of the fluid pressure. We present a variational approach to the direct problem and two reconstruction methods for the inverse problem, which are based on nonlinear optimization and regularization.
We consider the interaction between an elastic body and a compressible inviscid fluid, which occupies the unbounded exterior domain. The direct problem is to determine the scattered pressure field in the fluid domain as well as the displacement field in the elastic body, while the inverse problem is to reconstruct the shape of the elastic body from the far field pattern of the fluid pressure. We present a variational approach to the direct problem and two reconstruction methods for the inverse problem, which are based on nonlinear optimization and regularization.
2009年02月13日(金)
16:15-17:00 数理科学研究科棟(駒場) 270号室
Wenbin Chen 氏 (Fudan University)
New Energy-conserved Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations
Wenbin Chen 氏 (Fudan University)
New Energy-conserved Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations
[ 講演概要 ]
In this talk, two new energy-conserved splitting methods (EC-S-FDTDI and EC-S-FDTDII) for Maxwell’s equations are proposed. Both algorithms are energy-conserved, unconditionally stable and can be computed efficiently. The convergence results are analyzed based on the energy method, which show that the EC-S-FDTDI scheme is of first order in time and of second order in space, and the EC-S-FDTDII scheme is of second order both in time and space. We also obtain two identities of the discrete divergence of electric fields for these two schemes. For the EC S-FDTDII scheme, we prove that the discrete divergence is of first order to approximate the exact divergence condition. Numerical dispersion analysis shows that these two schemes are non-dissipative. Numerical experiments confirm well the theoretical analysis results.
In this talk, two new energy-conserved splitting methods (EC-S-FDTDI and EC-S-FDTDII) for Maxwell’s equations are proposed. Both algorithms are energy-conserved, unconditionally stable and can be computed efficiently. The convergence results are analyzed based on the energy method, which show that the EC-S-FDTDI scheme is of first order in time and of second order in space, and the EC-S-FDTDII scheme is of second order both in time and space. We also obtain two identities of the discrete divergence of electric fields for these two schemes. For the EC S-FDTDII scheme, we prove that the discrete divergence is of first order to approximate the exact divergence condition. Numerical dispersion analysis shows that these two schemes are non-dissipative. Numerical experiments confirm well the theoretical analysis results.
2009年02月10日(火)
15:00-16:00 数理科学研究科棟(駒場) 270号室
日時が2月10日に変わりましたのでご注意ください。
Piermarco Cannarsa 氏 (Univ. degli Studi Roma "Tor Vergata")
Carleman estimates for degenerate parabolic operators with application to null controllability
日時が2月10日に変わりましたのでご注意ください。
Piermarco Cannarsa 氏 (Univ. degli Studi Roma "Tor Vergata")
Carleman estimates for degenerate parabolic operators with application to null controllability
[ 講演概要 ]
From the controllability viewpoint, the behavior of uniformly parabolic equations is by now well understood. On the contrary, fewer results are known for degenerate parabolic equations, even though such a class of operators arise in many applied, as well as theoretical, problems.
A fairly complete analysis of the null controllability properties of degenerate parabolic equations in one space dimension was completed in a series of recent works by the speaker and coauthors. The aim of this talk is to review the above theory and present some recent results obtained in collaboration with P. Martinez and J.Vancostenoble for higher dimensional problems. Essential tools of such an approach are adapted Carleman estimates and Hardy type inequalities.
From the controllability viewpoint, the behavior of uniformly parabolic equations is by now well understood. On the contrary, fewer results are known for degenerate parabolic equations, even though such a class of operators arise in many applied, as well as theoretical, problems.
A fairly complete analysis of the null controllability properties of degenerate parabolic equations in one space dimension was completed in a series of recent works by the speaker and coauthors. The aim of this talk is to review the above theory and present some recent results obtained in collaboration with P. Martinez and J.Vancostenoble for higher dimensional problems. Essential tools of such an approach are adapted Carleman estimates and Hardy type inequalities.
2009年02月10日(火)
16:15-17:15 数理科学研究科棟(駒場) 270号室
日時が2月10日に変わりましたのでご注意ください。
Yurii Anikonov 氏 (Sobolev Institute of Mathematics)
Constructive methods in inverse problems
日時が2月10日に変わりましたのでご注意ください。
Yurii Anikonov 氏 (Sobolev Institute of Mathematics)
Constructive methods in inverse problems
[ 講演概要 ]
New representations for solutions and coefficients of evolutionary equations are presented. On the basic of these representations theorems of solvability for inverse problems are obtained. This direction develops constructibility in the theory and applications of inverse problems to differential equations
New representations for solutions and coefficients of evolutionary equations are presented. On the basic of these representations theorems of solvability for inverse problems are obtained. This direction develops constructibility in the theory and applications of inverse problems to differential equations
2009年02月06日(金)
16:15-17:00 数理科学研究科棟(駒場) 370号室
G. Yuan 氏 (Northeast Normal Univ.)
Inverse problems and observability inequalities for plate equations and Schrodinger equations.
G. Yuan 氏 (Northeast Normal Univ.)
Inverse problems and observability inequalities for plate equations and Schrodinger equations.
[ 講演概要 ]
In this talk, we will present some results on inverse problems and observability inequalities for some plate and Schrodinger equaions by using several kinds of Carleman estimates.
In this talk, we will present some results on inverse problems and observability inequalities for some plate and Schrodinger equaions by using several kinds of Carleman estimates.
2009年01月30日(金)
16:15-17:15 数理科学研究科棟(駒場) 370号室
F. Cakoni 氏 (University of Delaware)
Faber-Krahn Type Inequalities in Inverse Scattering Theory
F. Cakoni 氏 (University of Delaware)
Faber-Krahn Type Inequalities in Inverse Scattering Theory
[ 講演概要 ]
We first consider the scattering of time harmonic plane waves by a perfectly conducting infinite cylinder of cross section D. We observe that the Dirichlet eigenvalues for the Laplacian in D can be determined from the far field pattern of the scattered wave and hence from the Faber-Krahn inequality we can obtain a lower bound for the area of D. We then consider the corresponding problem for a dielectric medium. Here we observe that a relatively new type of spectra called transmission eigenvalues can be determined from the far field pattern of the scattered wave and show that transmission eigenvalues exist and form a discrete set. We then obtain a Faber-Krahn type inequality for transmission eigenvalues which, if D is known, provide a lower bound on the index of refraction n(x). Of special interest is the case when cavities may be present,i.e. regions where n(x)=1.We consider both isotropic and anisotropic materials.
We first consider the scattering of time harmonic plane waves by a perfectly conducting infinite cylinder of cross section D. We observe that the Dirichlet eigenvalues for the Laplacian in D can be determined from the far field pattern of the scattered wave and hence from the Faber-Krahn inequality we can obtain a lower bound for the area of D. We then consider the corresponding problem for a dielectric medium. Here we observe that a relatively new type of spectra called transmission eigenvalues can be determined from the far field pattern of the scattered wave and show that transmission eigenvalues exist and form a discrete set. We then obtain a Faber-Krahn type inequality for transmission eigenvalues which, if D is known, provide a lower bound on the index of refraction n(x). Of special interest is the case when cavities may be present,i.e. regions where n(x)=1.We consider both isotropic and anisotropic materials.
2009年01月30日(金)
15:10-16:10 数理科学研究科棟(駒場) 370号室
Lucie Baudouin 氏 (LAAS-CNRS groupe MAC)
Use of Carleman estimates for stability in some inverse problems
Lucie Baudouin 氏 (LAAS-CNRS groupe MAC)
Use of Carleman estimates for stability in some inverse problems
[ 講演概要 ]
In this presentation, we shall present how global Carleman inequalities can be used to prove the well-posedness of inverse problems related to various partial differential equations. This lecture will gather joint works with J.-P. Puel, A. Osses and A. Mercado. We focus here on stability results for the determination of potential from Neumann boundary measurements by using the Bukhgeim-Klibanov method. We will begin with the simplest models: the Schrodinger and wave equations, and then present some more recent results for transmission problems (same equations with discontinuous main coefficient).
In this presentation, we shall present how global Carleman inequalities can be used to prove the well-posedness of inverse problems related to various partial differential equations. This lecture will gather joint works with J.-P. Puel, A. Osses and A. Mercado. We focus here on stability results for the determination of potential from Neumann boundary measurements by using the Bukhgeim-Klibanov method. We will begin with the simplest models: the Schrodinger and wave equations, and then present some more recent results for transmission problems (same equations with discontinuous main coefficient).
2009年01月26日(月)
16:00-17:00 数理科学研究科棟(駒場) 470号室
Vilmos Komornik 氏 (University of Strasbourg)
Ingham-Beurling type inequalities
Vilmos Komornik 氏 (University of Strasbourg)
Ingham-Beurling type inequalities
[ 講演概要 ]
We present a self-contained constructive proof for a multidimensional generalization of Beurling's optimal condition for the validity of Ingham type estimates. We illustrate the usefulness of the result on a particular observability problem.
We present a self-contained constructive proof for a multidimensional generalization of Beurling's optimal condition for the validity of Ingham type estimates. We illustrate the usefulness of the result on a particular observability problem.
2009年01月09日(金)
16:00-17:00 数理科学研究科棟(駒場) 370号室
Leevan Ling 氏 (Hong Kong Baptist University)
Effective Condition Numbers and Laplace Equations
Leevan Ling 氏 (Hong Kong Baptist University)
Effective Condition Numbers and Laplace Equations
[ 講演概要 ]
The condition number of a matrix is commonly used for investigating the stability of solutions to linear algebraic systems. Recent meshless techniques for solving PDEs have been known to give rise to ill-conditioned matrices, yet are still able to produce results that are close to machine accuracy. In this work, we consider the method of fundamental solutions (MFS), which is known to solve, with extremely high accuracy, certain partial differential equations, namely those for which a fundamental solution is known. To investigate the applicability of the MFS, either when the boundary is not analytic or when the boundary data is not harmonic, we examine the relationship between its accuracy and the effective condition number.
The condition number of a matrix is commonly used for investigating the stability of solutions to linear algebraic systems. Recent meshless techniques for solving PDEs have been known to give rise to ill-conditioned matrices, yet are still able to produce results that are close to machine accuracy. In this work, we consider the method of fundamental solutions (MFS), which is known to solve, with extremely high accuracy, certain partial differential equations, namely those for which a fundamental solution is known. To investigate the applicability of the MFS, either when the boundary is not analytic or when the boundary data is not harmonic, we examine the relationship between its accuracy and the effective condition number.
