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Approximate cloaking for the heat equation via transformation optics

1 Department of Mathematics, EPFL SB CAMA, Station 8, CH-1015 Lausanne, Switzerland
2 Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

† This contribution is part of the Special Issue: Inverse problems in imaging and engineering science
   Guest Editors: Lauri Oksanen; Mikko Salo
   Link: https://www.aimspress.com/newsinfo/1270.html

Special Issues: Inverse problems in imaging and engineering science

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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Keywords heat equation; approximate cloaking; frequency analysis

Citation: Hoai-Minh Nguyen, Tu Nguyen. Approximate cloaking for the heat equation via transformation optics. Mathematics in Engineering, 2019, 1(4): 775-788. doi: 10.3934/mine.2019.4.775

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This article has been cited by

  • 1. Hoai-Minh Nguyen, Loc X. Tran, Approximate Cloaking for Time-dependent Maxwell Equations via Transformation Optics, SIAM Journal on Mathematical Analysis, 2019, 51, 5, 4142, 10.1137/18M1232395

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