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The book presents a deterministic homogenization theory intended for the mathematical analysis of non-stochastic multiscale problems, both within and beyond the periodic setting. The main tools are the so-called homogenization algebras, the classical Gelfand representation theory, and a class of actions by the multiplicative group of positive real numbers on numerical spaces. The basic approach is the Sigma-convergence method, which generalizes the well-known two-scale convergence procedure. Numerous problems are worked out to illustrate the theory and highlight its broad applicability. The book is primarily intended for researchers (including PhD students) and lecturers interested in periodic as well as non-periodic homogenization theory.
List of contents
- 1. Preliminaries. - 2. Homogenization Algebras on RN.- 3. Sigma-Convergence: The Periodic Setting.- 4. Sigma-Convergence: The General Setting.- 5. Homogenization of Elliptic Operators.- 6. Homogenization of Parabolic Operators I.- 7. Homogenization Of Parabolic Operators II.- 8. Reiterated Homogenization.
About the author
Gabriel Nguetseng was born in 1950 in Foto, Cameroon. He earned his PhD in 1984 from Université Pierre et Marie Curie, Paris 6. He was appointed Senior Lecturer in 1985 at the University of Yaoundé and promoted to Associate Professor six years later. Since 2004, he has served as a Professor of Mathematics. Gabriel Nguetseng is a co-initiator, along with Grégoire Allaire, of the well-known two-scale convergence theory, which underpins a widely used homogenization procedure. He has held visiting professor positions at several universities and research institutions and has been an invited speaker at numerous conferences. Additionally, he served as the organizer of the mini-symposium "Homogenization and its Applications" at ICIAM 2011 in Vancouver, Canada. He was the Secretary General of the Cameroonian Mathematical Society and the former Director of the University Center for Information Technology (Centre de Calcul) at the University of Yaoundé.
Summary
The book presents a deterministic homogenization theory intended for the mathematical analysis of non-stochastic multiscale problems, both within and beyond the periodic setting. The main tools are the so-called homogenization algebras, the classical Gelfand representation theory, and a class of actions by the multiplicative group of positive real numbers on numerical spaces. The basic approach is the Sigma-convergence method, which generalizes the well-known two-scale convergence procedure. Numerous problems are worked out to illustrate the theory and highlight its broad applicability. The book is primarily intended for researchers (including PhD students) and lecturers interested in periodic as well as non-periodic homogenization theory.
