On the homogenization of second order differential equations

Jiann Sheng Jiang*, Kung Hwang Kuo, Chi Kun Lin

*Corresponding author for this work

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4 Citations (Scopus)


We discuss the homogenization process of second order differential equations involving highly oscillating coefficients in the time and space variables. It generate memory or nonlocal effect. For initial value problems, the memory kernels are described by Volterra integral equations; and for boundary value problems, they are characterized by Fredholm integral equations. When the equation is translation (in time or in space) invariant, the memory or non-local kernel can be represented explicitly in terms of the Young's measure.

Original languageEnglish
Pages (from-to)215-236
Number of pages22
JournalTaiwanese Journal of Mathematics
Issue number2
Publication statusPublished - Jun 2005
Externally publishedYes


  • Dunford-Taylor integral
  • Eigenfunction expansion
  • Green's function
  • Homogenization
  • Kinetic formulation
  • Volterra and Fredholm integral equations
  • Weak limit
  • Young's measure

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