Abstract
The homogenization of the Dirac-like system is studied. It generates memory effects. The memory (or nonlocal) kernel is described by the Volterra integral equation. When the coefficient is independent of time, the memory kernel can be characterized explicitly in terms of Young's measure. The homogenized equation can be reformulated in the kinetic form by introducing the kinetic variable. We also characterize the memory kernel when the coefficient is of separable variable.
Original language | English |
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Pages (from-to) | 433-458 |
Number of pages | 26 |
Journal | Mathematical Models and Methods in Applied Sciences |
Volume | 11 |
Issue number | 3 |
DOIs | |
Publication status | Published - Apr 2001 |
Externally published | Yes |
Keywords
- Dirac-like system
- Dunford-Taylor integral
- Hergoltz function
- Homogenization
- Kinetic formulation
- Volterra integral equation
- Weak limits
- Young's measure