HOMOGENIZATION OF PARTIAL DIFFERENTIAL EQUATIONS
Review of Distributions, Sobolev spaces and Variational formulation. Introduction to Homogenization. Homogenization of elliptic PDEs. Specific Cases: Periodic structures and layered materials. Convergence Results: Energy method, Two-scale multi-scale methods, H-Convergence, Bloch wave method. General Variational convergence: G -convergence and G- convergence, Compensated compactness. Study of specific examples and applications
Books
- A. Bensoussan, J. L., Lions and G., Papanicolaon., Asymptotic Analysis for Periodic Structures, North Holland (1978).
- G. Dal Maso, An introduction to G � convergence, Birkauser (1993).
- V. V. Jikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of Differential Operators and Integral Functionals, Springer (1991).
- E. Sanchez � Palencia, Non homogeneous Media and Vibration Theory, Springer lecture Notes in Physics, 127 (1980).