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Approximate cloaking for the heat equation via transformation optics

Hoai-Minh Nguyen Tu Nguyen

*Corresponding author: Hoai-Minh Nguyen hoai-minh.nguyen@epfl.ch

MinE2019,4,775doi:10.3934/mine.2019.4.775

In this paper, we establish approximate cloaking for the heat equation via transformation optics. We show that the degree of visibility is of the order ε in three dimensions and |lnε|−1 in two dimensions, where ε is the regularization parameter. To this end, we first transform the problem in time domain into a family of problems in frequency domain by taking the Fourier transform with respect to time, and then derive appropriate estimates in the frequency domain.

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