Homogenization Theory for Multiscale Problems
Description
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.
Reviews / Votes
"This book also contains some classical results in functional analysis and in the analysis of partial differential equations collected in a useful appendix, which makes it self-contained. This book is an important contribution to the literature on homogenization theory. It is well written, remarkably clear, and mathematically accurate." (Mustapha El Jarroudi, Mathematical Reviews, February, 2026)
"The monograph is very well written and surely useful and accessible to a large audience. Therefore, in view of both the contents and the clarity of the presentation, the book is recommended to all pure or applied mathematicians interested into homogenization theory." (Paolo Musolino, zbMATH 1544.35004, 2024)
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Persons
Xavier Blanc is Professor at Université Paris Cité. His research has focused on the analysis of partial differential equations, and on numerical methods. Applications include superfluids, plasma physics, radiative transfer.
Claude Le Bris holds positions as Civil Engineer-General and Research Scientist at École des Ponts, as well as scientific leader of the MATHERIALS research team at Inria. He serves on several advisory boards of international research institutes and has extensive editorial responsibilities for book series and journals. His research has focused on mathematical analysis and numerical methods for partial differential equations, with contributions in several areas including the mathematics of computational chemistry and physics, multiscale problems and homogenization theory.
Content
1 In dimension "zero".- 2 Homogenization in dimension 1.- 3 Dimension = 2: The "simple" cases: abstract or periodic settings.- 4 Dimension = 2: Some explicit cases beyond the periodic setting.- 5 Numerical Approaches.- 6 Beyond the diffusion equation and miscellaneous topics.- Appendix A: Some basic elements of PDE analysis.