本計劃預計執行三年，主要的研究內容為固有值問題的研究和應用。其中包含 Sloshing problem 的固有值正反問題研究，BLT 分子螢光影像問題的鬆弛係數估計以 及最後一年的 Graph 上的 Sturm-Liouville 問題的正反問題的研究。其中 Sloshing problem 和 BLT 的數學模型雖為橢圓方程問題，但其固有係數 λ 是出現在邊界條件 上和傳統的 eigenvalues 極不相同。而 Ssturm-Liouville Problem on Graph 的研 究則是涉及多方面的應用，例如 scattering on networks, 為目前極多人專注的領域。 In this 3-year project, I will focus on the study of spectral problems and its applications. The three main subjects are: 1. The study of eigenvalues of the sloshing problems and its inverse problem, 2. The estimation of relax parameter on BLT, 3. The direct and inverse spectral problems on graphs. subject 1 and subject 2 are eigenvalue problems of elliptic differential equation with eigen-parameter on the boundary conditions, which is quite different from the classical boundary value problem. For the subject 3, we will deal with the direct and inverse spectral problems on graphs which are related to many topics, for an example, the scattering on networks. As we know, there are more and more researchers concentrating on s topic.
