Homogenization

Code: MA754 | L-T-P-C: 4-0-0-8

MA754 Homogenization L-T-P-C [4-0-0-8]

Elliptic operators, Dirichlet and periodic boundary conditions, asymptotic expansion using multiple scales, energy proof of the homogenization formula (Tartar's method of oscillating test functions), classical correctors, Bloch waves, Bloch expansion theorem, Bloch approximation function, homogenization of elliptic systems, composite materials containing high-modulus reinforcement, boundary layer theory in composite materials, asymptotic methods and spectral problems in fluid-solid structures, multiphase flows (solid-fluid mixture).

Texts/References:

1. A. Bensoussan, J.L. Lions, G. Papanicolaou, Asymptotic Analysis of Periodic Structure, North-Holland, Amsterdam, 1978.
2. N. Bakhvalov, G. Panasenko, Homogenisation: Averaging Process in Periodic Media, Kluwer Academic Publishers, Dordrecht, 1989.
3. D.Cioranescu, P. Donato, An Introduction to Homogenization, Oxford University Press, New York, 1999.
4. E.Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics, Vol. 127, Springer-Verlag, Berlin, 1980.
5. C. Conca, J.Planchard, M. Vanninathan, Fluid and Periodic Structures, John Wiley and Sons/Masson, Chichester, 1995.
6. G. Milton, The Theory of Composites, Cambridge University Press, Cambridge, UK, 2002.