Composite materials are widely used in industry and include such well known examples as superconductors and optical fibers. However, modeling these materials is difficult, since they often has different properties at different points. The mathematical theory of homogenization is designed to handle this problem. The theory uses an idealized homogenous material to model a real composite while taking into account the microscopic structure. This introduction to homogenization theory develops the natural framework of the theory with four chapters on variational methods for partial differential...

This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the College de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions.

The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control,...

This book presents the texts of selected lectures on recent work in the field of nonlinear partial differential equations delivered by leading international experts at the well-established weekly seminar held at the College de France. Emphasis is on applications to numerous areas, including control theory, theoretical physics, fluid and continuum mechanics, free boundary problems, dynamical systems, scientific computing, numerical analysis, and engineering. Proceedings of this seminar will be of particular interest to postgraduate students and specialists in the area of nonlinear partial...