Chiun-Chien Fu (Southern Taiwan University of Technology)
J.S. Jiang (Tung-Fang Institute of Technology)
Chun-Kong Law (NSYSU)
Wei-Cheng Lian (National Kaohsiung Marine University)
Wen-Ching Lien (NCKU)
Chi-Kun Lin (NCKU)
Tai-Chia Lin (CCU)
Tzon-Tzer Lu (NSYSU)
Jhi-Shen Tsay (NSYSU)
I-Mei Wang (National Ping-Tung Teachers' College)
Weichung Wang (NUK)
Chung-Fang Wu (Southern Taiwan University of Technology)
Topics:
Many differential equations come from physics. Analyzing those equations involve different mathematical theories and techniques. The corresponding results would be of immense physical interest. In this project, we shall study several problems in differential equations related to mathematical physics, mainly evolution problems and spectral problems.
Singular limits of differential equations and Homogenization:
We want to investigate singular limits problems related to the differential equations arising in mathematical physics. Emphasis will be on the incompressible limits of Euler-Poisson system and incompressible Euler limit of the Schrodinger-Poisson system. Homogenization of some mechanical systems will also be studied.
Analysis of some evolution equations:
We shall concentrate on the analysis of several important evolution equations, namely, equations related to fluid mechanics including Boltzmann equation, and Dirac-Klein-Gordan equation, harmonic map heat flow with rotational symmetry.
Inverse spectral problems:
We shall first concentrate on inverse spectral problems and inverse nodal problems on infinite intervals and bounded domains in Rn. We shall try to understand the triangular relations among the spectrum and nodal set and the Schrodinger operator. At the same time we shall study other related inverse problems such as matrix inverse eigenvalue problem, inverse scattering problems and crack problems. Probabilistic aspect will also be investigated.