DATE2021-11-25 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

TITLEWell-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.