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Approximate cloaking for the heat equation via transformation optics

  • Received: 26 November 2018 Accepted: 24 June 2019 Published: 29 August 2019
  • 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 $\varepsilon$ in three dimensions and $|\ln \varepsilon|^{-1}$ in two dimensions, where $\varepsilon$ 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.

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

    Related Papers:

  • 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 $\varepsilon$ in three dimensions and $|\ln \varepsilon|^{-1}$ in two dimensions, where $\varepsilon$ 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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