## FMSP Lectures

Seminar information archive ～09/27｜Next seminar｜Future seminars 09/28～

**Seminar information archive**

### 2016/11/04

10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)

The BV space in variational and evolution problems (3) (ENGLISH)

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

**Piotr Rybka**(the University of Warsaw)The BV space in variational and evolution problems (3) (ENGLISH)

[ Abstract ]

https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

[ Reference URL ]https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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

### 2016/11/04

13:00-14:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The BV space in variational and evolution problems (4) (ENGLISH)

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

**Piotr Rybka**(the University of Warsaw)The BV space in variational and evolution problems (4) (ENGLISH)

[ Abstract ]

https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

[ Reference URL ]https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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

### 2016/11/01

10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)

The BV space in variational and evolution problems (1) (ENGLISH)

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

**Piotr Rybka**(the University of Warsaw)The BV space in variational and evolution problems (1) (ENGLISH)

[ Abstract ]

https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

[ Reference URL ]https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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

### 2016/11/01

13:15-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

The BV space in variational and evolution problems (2) (ENGLISH)

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

**Piotr Rybka**(the University of Warsaw)The BV space in variational and evolution problems (2) (ENGLISH)

[ Abstract ]

https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

[ Reference URL ]https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照

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

### 2016/09/26

16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Mathematical Aesthetic Principles and Nonintegrable Systems (ENGLISH)

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

**Murray Muraskin**(University of North Dakota, Grand Forks)Mathematical Aesthetic Principles and Nonintegrable Systems (ENGLISH)

[ Abstract ]

The discussion presents a study of a set of mathematical principles that can be classified as "aesthetic”and shows that these principles can be cast into a set of nonlinear equations. The system of equations is nonintegrable in general. New techniques to handle the nonintegrability feature are discussed. We then illustrate how this system of equations leads to sinusoidal solutions, sine within sine solutions, the phenomenon known as beats, random type oscillations, two and three dimensional lattices, as well as multi wave packet systems. The sinusoidal solutions occur when the arbitrary data associated with the equations causes the equations to be linearized. The sinusoidal behavior totally disappears once the integrability equations are satisfied, illustrating how important the nonintegrability concept is to the development.

[ Reference URL ]The discussion presents a study of a set of mathematical principles that can be classified as "aesthetic”and shows that these principles can be cast into a set of nonlinear equations. The system of equations is nonintegrable in general. New techniques to handle the nonintegrability feature are discussed. We then illustrate how this system of equations leads to sinusoidal solutions, sine within sine solutions, the phenomenon known as beats, random type oscillations, two and three dimensional lattices, as well as multi wave packet systems. The sinusoidal solutions occur when the arbitrary data associated with the equations causes the equations to be linearized. The sinusoidal behavior totally disappears once the integrability equations are satisfied, illustrating how important the nonintegrability concept is to the development.

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

### 2016/08/12

15:00-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Multiscale simulations of waves and applications (ENGLISH)

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

**Eric Chung**(Chinese Univ. of Hong Kong)Multiscale simulations of waves and applications (ENGLISH)

[ Abstract ]

Numerical simulations of wave propagation in heterogeneous media are important in many applications such as seismic propagation and seismic inversion.

In this talk, we will present a new multiscale approach for seismic wave propagation.

The method is able to compute the solution with much fewer degrees of freedom compared with fine mesh simulation.

The idea is to capture the multiscale features of the solutions by carefully designed multiscale basis functions.

We will also present applications to inverse problems.

[ Reference URL ]Numerical simulations of wave propagation in heterogeneous media are important in many applications such as seismic propagation and seismic inversion.

In this talk, we will present a new multiscale approach for seismic wave propagation.

The method is able to compute the solution with much fewer degrees of freedom compared with fine mesh simulation.

The idea is to capture the multiscale features of the solutions by carefully designed multiscale basis functions.

We will also present applications to inverse problems.

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

### 2016/08/12

16:00-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Discrete regularization of parameter identification problems (ENGLISH)

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

**Christian Clason**(University Duisburg-Essen)Discrete regularization of parameter identification problems (ENGLISH)

[ Abstract ]

This talk is concerned with parameter identification problems where a distributed parameter is known a priori to take on values from a given set. This property can be promoted with the aid of a convex regularization term in the Tikhonov functional. We discuss the properties of minimizers of this functional and their numerical computation using a semismooth Newton method.

[ Reference URL ]This talk is concerned with parameter identification problems where a distributed parameter is known a priori to take on values from a given set. This property can be promoted with the aid of a convex regularization term in the Tikhonov functional. We discuss the properties of minimizers of this functional and their numerical computation using a semismooth Newton method.

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

### 2016/08/10

10:00-11:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Global-local-integration-based kernel approximation methods: Technical arguments (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hon2.pdf

**Benny Y C Hon**(City Univ. of Hong Kong)Global-local-integration-based kernel approximation methods: Technical arguments (ENGLISH)

[ Abstract ]

We discuss technical details of my talk on 8 Aug. and give also proofs of some main results.

[ Reference URL ]We discuss technical details of my talk on 8 Aug. and give also proofs of some main results.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hon2.pdf

### 2016/08/08

16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Global-local-integration-based kernel approximation methods (ENGLISH)

[ Reference URL ]

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

**Benny Y C Hon**(City Univ. of Hong Kong)Global-local-integration-based kernel approximation methods (ENGLISH)

[ Reference URL ]

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

### 2016/08/08

17:30-18:30 Room #128 (Graduate School of Math. Sci. Bldg.)

On the lifting of deterministic convergence results for inverse problems to the stochastic setting (ENGLISH)

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

**Daniel Gerth**(Tech. Univ. Chemnitz)On the lifting of deterministic convergence results for inverse problems to the stochastic setting (ENGLISH)

[ Abstract ]

In inverse problems, the inevitable measurement noise is modelled either by a deterministic worst-case model or a stochastic one.

The development of convergence theory in both approaches appears to be rather disconnected. In this talk we seek to bridge this gap and show how deterministic result can be transferred into the stochastic setting. The talk is split into two parts. In the first part, after briefly introducing "inverse problems" and the noise models, we examine the particular problem of sparsity-promoting regularization with a Besov-space penalty term to demonstrate the lifting technique. In the second part, we present a generalization of the technique that applies to a large group of regularization methods.

[ Reference URL ]In inverse problems, the inevitable measurement noise is modelled either by a deterministic worst-case model or a stochastic one.

The development of convergence theory in both approaches appears to be rather disconnected. In this talk we seek to bridge this gap and show how deterministic result can be transferred into the stochastic setting. The talk is split into two parts. In the first part, after briefly introducing "inverse problems" and the noise models, we examine the particular problem of sparsity-promoting regularization with a Besov-space penalty term to demonstrate the lifting technique. In the second part, we present a generalization of the technique that applies to a large group of regularization methods.

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

### 2016/06/23

15:00-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Complexity and Computability: Complex Dynamical Systems beyond Turing-Computability (ENGLISH)

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

**Klaus Mainzer**(Technische Universität München)Complexity and Computability: Complex Dynamical Systems beyond Turing-Computability (ENGLISH)

[ Abstract ]

The computational theory of complexity is founded by digital computing (e.g. Turing machine) which cannot fully grasp continuous concepts of mathematics. The mathematical theory of complex dynamical systems (with interdisciplinary applications in natural and economic sciences) is based on continuous concepts. Further on, there is an outstanding tradition in mathematics since Newton, Leibniz, Euler et al. with real algorithms in, e.g., numerical analysis. How can the gap between the digital and continuous world be mathematically overcome? The talk aims at mathematical and philosophical foundations and interdisciplinary applications of complex dynamical systems beyond Turing-computability.

[ Reference URL ]The computational theory of complexity is founded by digital computing (e.g. Turing machine) which cannot fully grasp continuous concepts of mathematics. The mathematical theory of complex dynamical systems (with interdisciplinary applications in natural and economic sciences) is based on continuous concepts. Further on, there is an outstanding tradition in mathematics since Newton, Leibniz, Euler et al. with real algorithms in, e.g., numerical analysis. How can the gap between the digital and continuous world be mathematically overcome? The talk aims at mathematical and philosophical foundations and interdisciplinary applications of complex dynamical systems beyond Turing-computability.

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

### 2016/05/09

15:00-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Vertex Operator Algebras according to Newton (ENGLISH)

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

**Michael Tuite**(National University of Ireland, Galway)Vertex Operator Algebras according to Newton (ENGLISH)

[ Abstract ]

In this lecture I will give an introduction to Vertex Operator Algebras (VOAs) using elementary methods originally due to Isaac Newton. I will also discuss a class of exceptional VOAs including the Moonshine module which share a number of fundamental properties in common.

[ Reference URL ]In this lecture I will give an introduction to Vertex Operator Algebras (VOAs) using elementary methods originally due to Isaac Newton. I will also discuss a class of exceptional VOAs including the Moonshine module which share a number of fundamental properties in common.

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

### 2016/04/21

15:00-16:00, 16:10-17:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Rational homotopy theory : Quillen and Sullivan approach.(2) (ENGLISH)

[ Reference URL ]

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

**Aniceto Murillo et al**(Universidad de Malaga)Rational homotopy theory : Quillen and Sullivan approach.(2) (ENGLISH)

[ Reference URL ]

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

### 2016/04/20

15:00-16:00, 16:10-17:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Rational homotopy theory : Quillen and Sullivan approach.(1) (ENGLISH)

[ Reference URL ]

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

**Aniceto Murillo et al**(Universidad de Malaga)Rational homotopy theory : Quillen and Sullivan approach.(1) (ENGLISH)

[ Reference URL ]

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

### 2016/04/14

15:30-17:00 Room #Lecture Hall, Kavli IPMU (Graduate School of Math. Sci. Bldg.)

Lecture 2: Geometric and algebraic Poisson modules (ENGLISH)

[ Reference URL ]

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

**Alan Weinstein**(University of California, Berkeley)Lecture 2: Geometric and algebraic Poisson modules (ENGLISH)

[ Reference URL ]

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

### 2016/04/13

13:30-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Determination of time-dependent coefficients for wave equations from partial data (ENGLISH)

[ Reference URL ]

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

**Yavar Kian**(Aix-Marseille Univ.)Determination of time-dependent coefficients for wave equations from partial data (ENGLISH)

[ Reference URL ]

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

### 2016/04/11

15:30-17:00 Room #Lecture Hall, Kavli IPMU (Graduate School of Math. Sci. Bldg.)

Lecture 1: Special subspaces in symplectic vector spaces (ENGLISH)

[ Reference URL ]

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

**Alan Weinstein**(University of California, Berkeley)Lecture 1: Special subspaces in symplectic vector spaces (ENGLISH)

[ Reference URL ]

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

### 2016/03/22

10:00-11:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Control and stabilization of degenerate wave equations (ENGLISH)

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

**Fatiha Alabau**(Université de Lorraine)Control and stabilization of degenerate wave equations (ENGLISH)

[ Abstract ]

The control of degenerate PDE's arise in many applications such as cloaking, climatology, population genetics, and vision.

For such models, the diffusion operator degenerates on some subset of the spatial domain. We present some recent results on observability, control and stabilization of these equations.

This is a joint work with Piermarco Cannarsa (University di Roma Tor Vergata, Italy) and G\"unter Leugering (Friedrich-Alexander-Universit\"at Erlangen-N\"urnberg, Erlangen, Germany).

[ Reference URL ]The control of degenerate PDE's arise in many applications such as cloaking, climatology, population genetics, and vision.

For such models, the diffusion operator degenerates on some subset of the spatial domain. We present some recent results on observability, control and stabilization of these equations.

This is a joint work with Piermarco Cannarsa (University di Roma Tor Vergata, Italy) and G\"unter Leugering (Friedrich-Alexander-Universit\"at Erlangen-N\"urnberg, Erlangen, Germany).

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

### 2016/03/22

11:00-12:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Stable determination of coefficients in the dynamical Schrödinger equation in a magnetic field (ENGLISH)

[ Reference URL ]

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

**Mourad Bellassoued**(Université de Tunis El Manar)Stable determination of coefficients in the dynamical Schrödinger equation in a magnetic field (ENGLISH)

[ Reference URL ]

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

### 2016/03/19

11:00-12:00 Room #370 (Graduate School of Math. Sci. Bldg.)

About the Landis conjecture (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov160319.pdf

**Oleg Emanouilov**(Colorado State Univ.)About the Landis conjecture (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov160319.pdf

### 2016/03/18

14:30-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Control of degenerate parabolic equations: old and new (ENGLISH)

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

**Piermarco Cannarsa**(Università degli Studi di Roma Tor Vergata)Control of degenerate parabolic equations: old and new (ENGLISH)

[ Abstract ]

This talk will survey the main results obtained in the last fifteen years or so for the null controllability of degenerate parabolic operators.

We shall describe the state of the art for operators which degenerate at the boundary as well as for certain classes of interior degeneracy of hypoelliptic type.

[ Reference URL ]This talk will survey the main results obtained in the last fifteen years or so for the null controllability of degenerate parabolic operators.

We shall describe the state of the art for operators which degenerate at the boundary as well as for certain classes of interior degeneracy of hypoelliptic type.

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

### 2016/02/22

17:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Inverse problems for parabolic operators : comparison of three different approaches (ENGLISH)

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

**Michel Cristofol**(Aix-Marseille Univ.)Inverse problems for parabolic operators : comparison of three different approaches (ENGLISH)

[ Abstract ]

Basing my talk around a toy problem : reconstruction of the potential for a linear parabolic problem, I will recall the two main classical following methods : Dirichlet to Neumann map and Carleman estimates. Then I will present a diﬀerent and recent approach based on pointwise observations and I will underline some points to be improved for each method. Then, I will finish my talk by a review of some results related to this technic of pointwise observations.

[ Reference URL ]Basing my talk around a toy problem : reconstruction of the potential for a linear parabolic problem, I will recall the two main classical following methods : Dirichlet to Neumann map and Carleman estimates. Then I will present a diﬀerent and recent approach based on pointwise observations and I will underline some points to be improved for each method. Then, I will finish my talk by a review of some results related to this technic of pointwise observations.

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

### 2016/02/19

10:30-11:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Recovering time-dependent inclusion in heat conductive bodies by a dynamical probe method (ENGLISH)

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

**Olivier Poisson**(Aix-Marseille University)Recovering time-dependent inclusion in heat conductive bodies by a dynamical probe method (ENGLISH)

[ Abstract ]

Many articles solve a version of the Calder'on inverse problem for the heat equation. The biggest part of them assume that the unknown conductivity do not depend on time t. But they are very few results concerning the time de- pendent situation, and they are based on the computation of an ansatz for the parabolic equation:

- A reconstruction method of an unknown moving inclusion by a dynamical probe method was performed by Daido-Kang-Nakamura in 2007, but it works for the one dimensional spatial space only,

- An energy estimate for x-multidimensional convex inclusions.

In the talk I will present a dynamical probe method based on special fundamental solutions of the heat equation and basic inequalities :

this approach is very close to the probe method for the elliptic Calderon inverse problem, and does not require regularity of the inclusion.

[ Reference URL ]Many articles solve a version of the Calder'on inverse problem for the heat equation. The biggest part of them assume that the unknown conductivity do not depend on time t. But they are very few results concerning the time de- pendent situation, and they are based on the computation of an ansatz for the parabolic equation:

- A reconstruction method of an unknown moving inclusion by a dynamical probe method was performed by Daido-Kang-Nakamura in 2007, but it works for the one dimensional spatial space only,

- An energy estimate for x-multidimensional convex inclusions.

In the talk I will present a dynamical probe method based on special fundamental solutions of the heat equation and basic inequalities :

this approach is very close to the probe method for the elliptic Calderon inverse problem, and does not require regularity of the inclusion.

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

### 2016/02/18

10:00-11:00 Room #002 (Graduate School of Math. Sci. Bldg.)

L^2 Extension and its applications: A survey (3) (ENGLISH)

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

**Dror Varolin**(Stony Brook)L^2 Extension and its applications: A survey (3) (ENGLISH)

[ Abstract ]

We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.

The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.

The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.

The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.

[ Reference URL ]We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.

The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.

The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.

The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.

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

### 2016/02/18

10:30-11:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Inverse boundary value problem for a hyperbolic equation in an infinite guide (ENGLISH)

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

**Michel Cristofol**(Aix-Marseille Univ.)Inverse boundary value problem for a hyperbolic equation in an infinite guide (ENGLISH)

[ Abstract ]

We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove Holder stability with the aid of a Carleman estimate specially designed for hyperbolic waveguides. I will provide numerical simulations in multiple backgrounds.

[ Reference URL ]We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove Holder stability with the aid of a Carleman estimate specially designed for hyperbolic waveguides. I will provide numerical simulations in multiple backgrounds.

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