# Takeshi Fukao, Department of Mathematics, Kyoto University of Education

オフィスアワーはこちら
HOME　＞　研究　＞　招待・特別講演

## 研究Research

### 国内/国際会議　招待/特別講演 数学

#### 招待講演: 国際会議「Free Boundary Problems: Theory and Applications」

2017年7月9日から7月14日、中国上海の上海交通大学で行われた国際会議「Free Boundary Problems: Theory and Applications」にて講演を行いました。

#### 招待講演: INdAM meeting OCERTO 2016

2016年6月20日から6月24日、イタリアのコルトナで行われた国際会議「INdAM meeting OCERTO 2016」にて講演を行いました。

To investigate recent issues arising in connection with optimal control problems and their ramifications and applications in many different fields, including aerospace, process control, bioengineering, economics and finance, and phase transformations. Related issues as inverse problems, optimization methods, the mathematical analysis of the state systems, their approximation and related computations are also very intriguing and will be considered. Sliding mode control will be one interesting topic for our Conference. The difficulty and complexity of the related problems require the contribution of experts from different areas. The purpose of the conference is hence to stimulate an interdisciplinary discussion and to review the recent developments in the field.

### 国内/国際会議 招待/特別講演 数学教育

#### 招待講演: 数学教育学会 2019年度数学教育学会 秋季例会

オーガナイズドセッションA「解析教育の課題と展望」

#### 招待講演: 9th International Conference onScience and Mathematics Education in Developing Countries

2016年11月4日から11月6日、ミャンマーのマンダレー大学で行われた国際会議「第9回発展途上国における科学と数学教育会議」にて講演を行いました。

This is the ninth in a series of conferences on mathematics and mathematics education, aimed at promoting mathematics and mathematics education in the Southeast Asian region, with particular focus on Myanmar, Cambodia and Laos. In particular, the 9th ICSMEDC hopes together mathematicians from around the globe to The Republic of the Union of Myanmar to discuss how to enhance mathematical activities in the nation and facilitate exchange and collaboration among mathematicians and mathematics educators from Myanmar, other Southeast Asian countries, and beyond. It will provide a venue for researchers and educators to meet, share ideas and experiences, form connections and community. The conference will be held in cooperation with the Mathematical Society of Myanmar, the Southeast Asian Mathematical Society and the American Mathematical Society.

#### 招待講演: 数学教育学会 2013年度数学教育学会 春季年会

オーガナイズドセッションB「小学校・中学校教員に必要な数学」

### セミナー 招待/特別講演 数学

#### 招待講演: I.M.A.T.I. - C.N.R. Applied Mathematics Seminar

2019年2月13日、パヴィア大学で行われた「Applied Mathematics Seminar」にて講演を行いました。

In this talk we concerned with the long time behavior of the solution to an equation and dynamic boundary condition of Cahn-Hilliard type with the logarithmic potential. This system is constructed by Cahn-Hilliard system in the bulk and on the boundary, and has a structure of the total mass conservation, namely the volume in the bulk puls the boundary. Firstly we obtain the regularity results and then we can prove the separation property from pure phase. Secondly, we discuss the characterization of the $\omega$-limit set, namely subsequence convergence to an stationary solution. Finally, by applying the extended Lojasiewicz-Simon inequality we can prove that the $\omega$-limit set consists only one point. This study is joint work with Hao Wu (Fudan University, China).

#### 特別講演: 第4回数理科学夏季若手研究会

2018年9月9日-10日、名城大学で行われた第4回数理科学夏季若手研究会にて講演を行いました。

#### 招待講演: 応用数学セミナー

2018年6月14日、東北大学で行われた「応用数学セミナー」にて講演を行いました。

#### 招待講演: 復旦大学数学科学学院 数学総合報告会

2018年3月7日、中国上海の復旦大学で行われた「復旦大学数学科学学院 数学総合報告会」で講演を行いました。

In this talk, recent advances in Cahn–Hilliard system with dynamic boundary condition of GMS type is treated. There are various studies of Cahn–Hilliard system with dynamic boundary condition. In 2011, G. R. Goldstein, A. Miranville and G. Schimperna introduced some equation and dynamic boundary condition of Cahn–Hilliard type. This system is constructed by Cahn–Hilliard system in the bulk and on the boundary, and has a structure of the total mass conservation, namely the volume in the bulk puls the boundary. Taking account of this structure, the well-posedness for GMS type was discussed for wider setting of potential in 2015. The first part of this talk is devoted to the above introduction. In the second part, the well-posedness of degenerate parabolic equation with dynamic boundary condition is discussed. The essential idea is to characterize the target degenerate parabolic equation as the asymptotic limit of Cahn–Hilliard system of GSM type. The approximate problem of Cahn–Hilliard systems can be solved with suitable uniform estimates. The growth condition of the maximal monotone graph with related to nonlinear diffusion term is a point of emphasis. The related topics are also treated in the last part. This study is based on the recent joint works with P. Colli (Pavia, Italy).

#### 招待講演: Trends in variational evolution

2018年2月21日、オーストリア ウィーン大学で行われた ワークショップ「Trends in variational evolution」で講演を行いました。

Variational evolution problems are almost ubiquitous in applications and have been considered in connection with fluid dynamics, phase transitions, thin films, quantum models, nonlinear diffusion and transport problems, chemical reactions, rate-independent phenomena, and material modeling, just to mention a few hot topics. The workshop is intended to present contemporary research directions in variational evolution models and methods.

In this talk, recent advances in equation and dynamic boundary condition of Cahn-Hilliard type are treated. There are various studies of Cahn-Hilliard systems with dynamic boundary condition. In 2011, some equation and dynamic boundary condition of Cahn-Hilliard type (GMS model) was introduced. This system is constructed by a Cahn-Hilliard system in the bulk and on the boundary, d has a structure of total mass conservation, namely the volume in the bulk plus the boundary. Taking account of this structure, the well-posedness for GMS model was discussed for a wider setting of potentials in 2015. The first part of this talk is devoted to the above introduction. In the second part, the well-posedness of a degenerate parabolic equation with dynamic boundary condition is discussed. The essential idea is to characterize the target degenerate parabolic equation as the asymptotic limit of Cahn-Hilliard system of GSM model. The approximate problem Cahn-Hilliard systems can be solved with suitable uniform estimates. The growth condition of the maximal monotone graph related to a nonlinear diffusion term is a point of emphasis. The related topics are also treated in the last part.

#### 招待講演: 第8回拡散と移流の数理

2017年9月5日、福岡大学で行われた「第8回拡散と移流の数理」にて講演を行いました。

#### 招待講演: 岐阜数理科学セミナー

2017年6月23日、岐阜大学で行われた岐阜数理科学セミナーにて講演を行いました。

#### 招待講演: 表面・界面ダイナミクスの数理13

2017年4月19日から4月21日、東京大学大学院数理科学研究科で行われたFMSP チュートリアルシンポジウム/ 数理科学連携基盤センター共催「表面・界面ダイナミクスの数理13」にて講演を行いました。

#### 招待講演: Special Afternoon on Diffuse Interface Models and Related Problems

2017年2月7日、イタリアのパヴィア大学で行われたApplied Mathematics Seminar「Special Afternoon on Diffuse Interface Models and Related Problems」にて講演を行いました。

The well-posedness for a system of partial differential equations and dynamic boundary conditions is discussed. This system is a sort of transmission problem between the dynamics in the bulk and on the boundary. The Poisson equation for the chemical potential, the Allen--Cahn equation for the order parameter in the bulk are considered as auxiliary conditions for solving the Cahn--Hilliard equation on the boundary. Recently the well-posedness for the equation and dynamic boundary condition, both of Cahn--Hilliard type, was discussed. Based on this result, the existence of the weak solution and its continuous dependence on the data are proved.This study is based on the recent joint works with P. Colli (Pavia, Italy).

#### 招待講演: Perspectives in Applied PDEs: a day in Pavia

2016年2月9日、イタリアのパヴィア大学で行われたセミナー「Perspectives in Applied PDEs: a day in Pavia」にて講演を行いました。

#### 招待講演: Dissipative models in phase transitions

2004年9月5日から11日にかけて、イタリア コルトナで行われた ワークショップ「Dissipative models in phase transitions」にて講演を行いました。