University of Birmingham > Talks@bham > Analysis seminar > Homogenisation of high-contrast PDE and two-scale Gamma-convergence

Homogenisation of high-contrast PDE and two-scale Gamma-convergence

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If you have a question about this talk, please contact Neal Bez.

The talk will begin with an outline of the ``mathematical theory of homogenisation’’, which studies partial differential equations (PDE) with rapidly oscillating data.

The classical results in this area (from the early 1970s) concern second-order PDE that are uniformy elliptic, and the related theory is well developed, including nonlinear settings via the so-called Gamma convergence for variational integrals. It can be shown however, that introducing a high degree of contrast into such problems, thus violating the assumption of uniform ellipticity, may result in homogenised limits of a non-standard (or ``non-classical’‘) kind.

The main focus of the talk will be on nonlinear variational problems with high contrast. In order to pass to the homogenisation limit in such problems, we introduce the concept of ``two-scale Gamma-convergence’’. I will discuss various properties of the limiting integral and their implications for the mechanics of composite materials.

This is joint work with Mikhail Cherdantsev.

This talk is part of the Analysis seminar series.

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