One-Day Workshop in PDEs
【One-Day Workshop in PDEs】
● 日期: 2017年1月5日 星期四
● 地點: 國立中央大學鴻經館M107
● Program :
10:00 ~11:00 Prof. Shouhong Wang (Indiana University)
Title: PID Cosmological Model
Abstract: We demonstrate that the phenomena of dark matter and dark
energy, together with the quark confinement and the Higgs field,
leads us to propose the principle of interaction dynamics (PID).
Intuitively, PID takes the variation of the Lagrangian action under
energy-momentum conservation constraint. With PID, we derive new
gravitational field equations, altering the Einstein equations with a
new term analytically derived from the constraints. The new field
equations provide a natural cosmological model, and offer different
insights to the structure of the universe. This is joint work with
Tian Ma.
11:10~12:10 Prof. I-Kun Chen (Kyoto University)
Title:Singularity and Regularity for the stationary solution to linearized Boltzmann equations
Abstract: In Boltzmann equation, the interplaying between free transport,
collision, and boundary yields rich phenomena in regularity of
solutions. In this talk, we will first introduce the logarithmic
singularity both on macroscopic microscopic variables due to the
boundary. Then, we will discuss the regularity of stationary solution
in convex domain. Finally, we will provide the analysis that realize
our observation.
14:00~15:00 Prof. Tien-Tsan Shieh (National Taiwan University)
Title: Fractional (Nonlocal) partial differential equation and calculus of variation
Abstract: In this talk, we study a new class of fractional partial differential equations which are obtained by minimizing variational problems in fractional Sobolev spaces. We introduce a notion of fractional gradient which has the potential to extend many classical results in Sobolev spaces to a nonlocal and fractional setting in a natural way. In the beginning, I will give a short introduction to the fractional calculus. Some regularity issues will be discussed in my talk.
3:20~4:20 Dr. Shih-Wei Chou (National Central University)
Title: Well-posedness of Transonic Fanno-Rayleigh Flows.