Fri, February 14, 2020
Public Access Category: All |
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- Time:
- 2:30pm-3:30pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Partial Differential Equations seminar.
Speaker: Vivek Tewary.
Affiliation: IIT Bombay.
Date and Time: Friday 14 February, 02:30 pm - 03:30 pm.
Venue: Room 114, Department of Mathematics.
Title: Bloch wave approach to almost periodic homogenization.
Abstract: Bloch wave homogenization is a spectral method for obtaining
effective coefficients for periodically heterogeneous media. This method
hinges on the direct integral decomposition of periodic operators, which
is not available in a suitable form for almost periodic operators. In
particular, the notion of Bloch eigenvalues and eigenvectors does not
exist for almost periodic operators. However, we are able to recover the
homogenization result in this case, by employing a sequence of periodic
approximations to almost periodic operators. Another approach, that
employs periodic lifting of quasiperiodic operators is also discussed. We
also establish a rate of convergence for approximations of homogenized
tensors for a class of almost periodic media