此計畫研究相關於 Maxwell系統之均質化(homogenization). 此均質化會產生記憶效應(memory effects). 此記憶核(memory kernel)可藉由 Volterra 積分方程描述, 記憶核更可藉由 Young』s 測度確切的表現出來, 並可由均質化方程獲得動態表現式。The purpose of this paper is to study the memory (or nonlocal) effect induced by homogenization of the Maxwell's type system. The memory kernel is described by the Volterra integral equation. Furthermore, it can be characterized explicitly in terms of Young's measure, and the kinetic formulation of the homogenized equation is also obtained. The kinetic formulation allows us to obtain the homogenization of the energy density and the associated conservation law with the Poynting vector. The interesting interaction phenomenon of the microscopic and macroscopic scales is also discussed and the memory effect explains qualitatively something about irreversibility.
