## Taiwanese Journal of Mathematics

### ON THE HOMOGENIZATION OF SECOND ORDER DIFFERENTIAL EQUATIONS

#### Abstract

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 nonlocal kernel can be represented explicitly in terms of the Young's measure.

#### Article information

Source
Taiwanese J. Math., Volume 9, Number 2 (2005), 215-236.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500407797

Digital Object Identifier
doi:10.11650/twjm/1500407797

Mathematical Reviews number (MathSciNet)
MR2142574

Zentralblatt MATH identifier
1077.35020

#### Citation

Jiang, Jiann-Sheng; Kuo, Kung-Hwang; Lin, Chi-Kun. ON THE HOMOGENIZATION OF SECOND ORDER DIFFERENTIAL EQUATIONS. Taiwanese J. Math. 9 (2005), no. 2, 215--236. doi:10.11650/twjm/1500407797. https://projecteuclid.org/euclid.twjm/1500407797

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