ncku-talk2021-11-25

Colloquium

DATE 2021-11-25　16:10-17:00

PLACE 化學館 36104教室

SPEAKER 王振男教授（國立台灣大學數學系）

TITLE Well-Posedness vs Ill-Posedness in PDEs

ABSTRACT When dealing with direct problems in PDEs, we normally expect that the problems are well-posedness, i.e., there exists a unique solution and the solution depends continuously on data. However, for most inverse problems, well-posedness may fail. We may be able to prove the uniqueness of the problem. But the continuous dependence does not hold in the usual sense. In this talk, I would like to discuss some interesting phenomena of continuous dependence in several inverse problems. In some cases, I will also show that the continuous dependence will improve in high frequency. We will view the increasing stability phenomenon from the viewpoints of stability and instability estimates.

Colloquium

DATE	2021-11-25　16:10-17:00

PLACE	化學館 36104教室

SPEAKER	王振男教授（國立台灣大學數學系）

TITLE	Well-Posedness vs Ill-Posedness in PDEs

ABSTRACT	When dealing with direct problems in PDEs, we normally expect that the problems are well-posedness, i.e., there exists a unique solution and the solution depends continuously on data. However, for most inverse problems, well-posedness may fail. We may be able to prove the uniqueness of the problem. But the continuous dependence does not hold in the usual sense. In this talk, I would like to discuss some interesting phenomena of continuous dependence in several inverse problems. In some cases, I will also show that the continuous dependence will improve in high frequency. We will view the increasing stability phenomenon from the viewpoints of stability and instability estimates.