MA 344: Homogenization of Partial Differential Equations

Credits: 3:0

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:

  1. A. Bensoussan, J. L., Lions and G., Papanicolaon., Asymptotic Analysis for Periodic Structures, North Holland (1978).
  2. G. Dal Maso, An introduction to $\\Gamma$ convergence, Birkauser (1993).,
  3. V. V. Jikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of Differential Operators and Integral Functionals, Springer (1991).
  4. E. Sanchez Palencia, Non homogeneous Media and Vibration Theory, Springer lecture Notes in Physics, 127 (1980).

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 14 Jul 2024