Approximate cloaking for the heat equation via transformation optics

Hoai-Minh Nguyen; Tu Nguyen

doi:10.3934/mine.2019.4.775

Mathematics in Engineering, 2019, 1(4): 775-788. doi: 10.3934/mine.2019.4.775. Research article Special Issues

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Approximate cloaking for the heat equation via transformation optics

Hoai-Minh Nguyen, Tu Nguyen

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

Received: , Accepted: , Published:

Special Issues: Inverse problems in imaging and engineering science

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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
2. Lauri Oksanen, Mikko Salo, Inverse problems in imaging and engineering science, Mathematics in Engineering, 2020, 2, 2, 287, 10.3934/mine.2020014

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