# 李大潛教授

## 香港城市大學香港高等研究院資深院士

## 上海復旦大學教授

## 中國科學院院士

## 世界科學院院士

## 法國科學院外籍院士

## 聯絡資料

電郵: | dqli@fudan.edu.cn |
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網址: | 個人網頁 |

Professor Li Tatsien (Li Daqian) is one of the best specialists, worldwide, of the theory and numerical analysis of nonlinear hyperbolic partial differential equations, a domain where major difficulties abound, as well as a domain of fundamental importance in applications. These include in particular nonlinear elasticity and gas dynamics. For all his contributions to these fields, Professor Li has been elected to five national or international Academies, and he has received numerous prestigious awards and honors.

Guided by the objective of acquiring a better understanding of the theory and physics of shocks that occur in gas dynamics, Professor Li has developed a new theory of local existence of classical and discontinuous solutions for the most general quasi-linear hyperbolic systems with two variables, including those where a free boundary occurs. In this fashion, he was able to specify the local structure of discontinuous solutions. This pioneering work immediately attracted the attention of the best specialists of the subject.

In another series of fundamental contributions, Professor Li has established the existence of classical solutions for the Cauchy problem for general quasi-linear hyperbolic systems, with "sufficiently small" initial data. This work constitutes a double achievement: First, it provides optimal estimates of lower and upper bounds for the "life-span" of a classical solution; second, it can be applied to the system of nonlinear elastodynamics. The late Professor Jean Leray, one of the most famous mathematicians of the twentieth century, then made the following comment on this work: [quote] "The work of Li Tatsien provides precise and elegant answers to manifold questions raised by many researchers" [unquote]. More recently, Professor Li was able to obtain the first satisfactory mathematical modeling of "diagraphy of wells by resistivity", a method of fundamental importance in petroleum exploitation. This work led him to introduce a new family of boundary value problems, called "boundary value problems with equipotential surface". He then studied such problems, both theoretically and numerically, in particular by successfully applying homogenization theory to the modeling of an electrod composed of many parts. It is a measure of the success and power of his approach that it is currently used in more than ten petroleum fields over the world!

Professor Li is not only an eminent mathematician. During the past decades, he has been extremely influential in the development of the pure and applied mathematical community. In particular, a very far-sighted initiative was taken in 1998 by the late Jacques-Louis Lions, one of the most prominent applied mathematician of the twentieth century, and Professor Li, who together co-founded the ISFMA, the Institut Sino-Francais de Mathematiques Appliquees, or Chinese-French Institute of Applied Mathematics.

Thanks to the tireless efforts of Professor Li, this Institute, which is housed on the campus of Fudan University, has organized every year since 1998 highly successful Summer Schools, which have considerably contributed to the promotion and development of "modern" pure and applied mathematics in Asia and in the rest of the world.

Guided by the objective of acquiring a better understanding of the theory and physics of shocks that occur in gas dynamics, Professor Li has developed a new theory of local existence of classical and discontinuous solutions for the most general quasi-linear hyperbolic systems with two variables, including those where a free boundary occurs. In this fashion, he was able to specify the local structure of discontinuous solutions. This pioneering work immediately attracted the attention of the best specialists of the subject.

In another series of fundamental contributions, Professor Li has established the existence of classical solutions for the Cauchy problem for general quasi-linear hyperbolic systems, with "sufficiently small" initial data. This work constitutes a double achievement: First, it provides optimal estimates of lower and upper bounds for the "life-span" of a classical solution; second, it can be applied to the system of nonlinear elastodynamics. The late Professor Jean Leray, one of the most famous mathematicians of the twentieth century, then made the following comment on this work: [quote] "The work of Li Tatsien provides precise and elegant answers to manifold questions raised by many researchers" [unquote]. More recently, Professor Li was able to obtain the first satisfactory mathematical modeling of "diagraphy of wells by resistivity", a method of fundamental importance in petroleum exploitation. This work led him to introduce a new family of boundary value problems, called "boundary value problems with equipotential surface". He then studied such problems, both theoretically and numerically, in particular by successfully applying homogenization theory to the modeling of an electrod composed of many parts. It is a measure of the success and power of his approach that it is currently used in more than ten petroleum fields over the world!

Professor Li is not only an eminent mathematician. During the past decades, he has been extremely influential in the development of the pure and applied mathematical community. In particular, a very far-sighted initiative was taken in 1998 by the late Jacques-Louis Lions, one of the most prominent applied mathematician of the twentieth century, and Professor Li, who together co-founded the ISFMA, the Institut Sino-Francais de Mathematiques Appliquees, or Chinese-French Institute of Applied Mathematics.

Thanks to the tireless efforts of Professor Li, this Institute, which is housed on the campus of Fudan University, has organized every year since 1998 highly successful Summer Schools, which have considerably contributed to the promotion and development of "modern" pure and applied mathematics in Asia and in the rest of the world.