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).