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 :

  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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E-mail: chairman.math[at]iisc[dot]ac[dot]in