Blanc X. Homogenization Theory for Multiscale Problems. An Introduction 2023

Textbook in PDF format

The book provides a pedagogic and comprehensive introduction to homogenization theory with a special focus on problems set for non-periodic media. The presentation encompasses both deterministic and probabilistic settings. It also mixes the most abstract aspects with some more practical aspects regarding the numerical approaches necessary to simulate such multiscale problems. Based on lecture courses of the authors, the book is suitable for graduate students of mathematics and engineering.
In Dimension “Zero”
Homogenization in Dimension 1
Dimension > 2: The “Simple” Cases: Abstract or Periodic Settings
Dimension > 2: Some Explicit Cases Beyond the Periodic Setting
Numerical Approaches
Beyond the Diffusion Equation and Miscellaneous Topics