MA 344: 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
Suggested books and references:
A. Bensoussan, J. L., Lions and G., Papanicolaon., Asymptotic Analysis for Periodic Structures, North Holland (1978).
G. Dal Maso, An introduction to $\\Gamma$ 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).