此計畫主要研究網格型動態系統及反映擴散方程行波解的交互作用及其穩定性問題。我們預計利用加權能量估計、比較理論、譜分析及Evans函數等方法研究行波解的其穩定性問題。此外、我們將探討來自於不同類型行波解交互作用下各類整體解的存在性及其性質、期能對於模型波的傳遞現象能有更進一步之理解。 ;This project is concerned with the interaction and stability of traveling wave solutions for lattice dynamical systems and reaction-diffusion equations. We plan to use the weighted energy estimate, comparison theorem, spectrum analysis and the technique of Evans function to study the stability problem of traveling wave solutions. In addition, we look for the existence and properties of different entire solutions originating from multiple traveling fronts, which can exhibit new characteristic behaviors in the front dynamics.
