臺灣大學數學系演講
博士生論文口試

 
演講者：林奕亘
講  題：The development of the Enclosure Method in an Anisotropic Background and the Strong Unique Continuation for the Elasticity with Residual Stress
時  間：2015年12月23日 (星期三) 17:20
地  點：臺灣大學天數館440室
摘  要：
    The goal of this dissertation is to develop reconstruction schemes to determine penetrable and impenetrable obstacles in a region in 3-dimensional in an anisotropic background. We demonstrate the enclosure-type method for two different mathematical models: The anisotropic elliptic equation and the anisotropic Maxwell system. So far, in the anisotropic case, there are no complex geometrical optics solutions which we can use to reconstruct the unknown obstacles in a given medium. Therefore, we use another special type solution: the oscillating decaying solutions, which are useful in our inverse problems. 
    In particular, for the anisotropic Maxwell system model, we also introduce a new reduction method to transform the Maxwell system into a second order strongly elliptic system. This reduction method is the main tool to construct the oscillating decaying solutions for the anisotropic Maxwell system. In addition, we prove the strong unique continuation for a residual stress system with Gevrey coefficients.