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宝威体育(中国)集团有限公司题目: 院士讲坛第三十三期:Remarks on Ill-Posed and Well-Behaved PDE Problems
报 告 人: 林芳华
宝威体育(中国)集团有限公司人所在单位: 美国纽约大学柯朗研究所
宝威体育(中国)集团有限公司日期: 2023-06-28
宝威体育(中国)集团有限公司时间: 14:00-15:00
宝威体育(中国)集团有限公司地点: 复旦大学邯郸校区 光华楼西辅楼407
   
宝威体育(中国)集团有限公司摘要:

The notion of Well-Posedness for PDE problems goes back to Hadamard which is commonly phrased into three properties for solutions: 1) existence; 2) uniqueness; 3) continuous dependence. In the mid-1950s,

F. John introduced a notion of Well-Behaved PDE problems. This latter seems to be more relevant to numerical approximations, machine-learnings and data analysis. What may be more interesting is that Ill-Posed problems could be Well-Behaved and Well-posed ones may be Ill-Behaved; and these properties may not necessarily depend on only the types of equations but also on the specificity of problems and geometry of data involved.

In this lecture, I will illustrate these notions and properties of solutions through several examples for the simplest linear PDEs. For similar problems in highly heterogeneous, oscillating media (or with stochastic noise), there are some recent progress and many interesting open questions.

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本年度学院宝威体育(中国)集团有限公司总序号: 14

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